Yes, but it was way down the list of war aim priorities. Eastern and Western Europe came first, then came Africa, and then came everything else, which includes Asia. This program published in the Deutsche Kolonial-Zeitung, a newspaper dedicated to colonial issues, shows that pretty clearly:

An extension of her territory proper in Europe imposes on the empire on the German people as close a union as possible in politics, military science and economics with the friendly states of Central Europe; none the less; the possession of colonies proper is an absolute necessary complement to a European Germany; this possession will make of her a friend for her allies ever so much more precious both economically and politically.

Or in the words of Fritz Fischer, the eminent scholar on Germany’s ambitions before and during WWI:

It is true that the colonial questions did not figure largely in the discussions on Germany’s war aims; it was generally assumed that if Germany won the war they would practically realise themselves. The foreground of these discussions was occupied by European questions which were regarded as the foundation for any overseas policy.

That especially means that there wasn’t really an overarching plan for Asia; if it was mentioned, it was a part of larger initiatives for war aims, which there were a lot of in Germany during WWI. The colonial plans also constantly kept changing depending on who you asked when about what, so I’ll deliver a short overview over the relevant proposals I could find and try to provide some context.

In November 1916, the Admiralty submitted a proposal that called for the return of German New Guinea, the Bismarck Archipelago, and the island of Yap. Since all German colonies were sooner or later occupied during WWI – and in the Pacific, where all colonies were small in terms of area, population, or both, this meant sooner – nearly all proposals called for the return of those occupied colonies (we’ll get to an interesting exception later). Additionally, there should be a "peaceful acquisition" of one of the large islands of Dutch East India, though this is more fanciful dreaming than a war aim per se. This proposal was adopted by Hindenburg and Chancellor Bethmann-Hollweg and communicated to US president Wilson as part of a "minimal demands" response to one of the odd peace initiatives.

In May 1917, Admiral von Holtzendorff let Kaiser Wilhelm II. know about some other ideas he had had after discussion with the colonial ministry. Most especially, this included the general idea of a system of bases around the world, designed to make it impossible for Germany’s enemies to ever seriously threaten it again. To quote from the Deutsche Kolonial-Zeitung again:

Besides a fleet, [the] military and economic security of our foreign and colonial territory requires the possession of strategic points, notably a sufficient number of coaling stations, submarine telegraphs and cables, with fortifications as required.

In the South Sea, that meant a new base for a wireless station, potentially in Portuguese Timor. Additionally, New Caledonia should potentially be taken over for its nickel and cobalt reserves. New Guinea and the Bismarck archipelago should also be returned.

Holtzendorff also included some thoughts on China, where he preferred more concessions “on the pattern” of the concessions in Tianjin and Hankou to military bases. For this, he considered Wuhu, “a place in South China, the choice to be dictated by purely commercial commercial considerations”, or, strangely enough, Qingdao. Strangely, because Qingdao had since 1897 already been under German administration, and Germany would continue to claim it even after the treaty of Versailles.

Maybe one thought that was flying around in the upper ranks of government can make of sense of that: Apparently, it was considered to give up Qingdao to the Japanese, who had been occupying it since 1914 anyway, to facilitate a rapprochement between the two powers. While this would have meant giving up the only actual colony Germany had in China, at this point Qingdao had basically become a bit of burden anyway, since it had become obvious that even though Germany had invested more in that one town than in its other colonies combined, the hoped-for trade basis was simply not materialising. Still, the government did not want to give up its dreams of 400 million potential Chinese customers for German goods for a "large, less developed Central Africa". Same for the Deutsche Kolonial-Zeitung:

Attractive as the idea appears of being limited to a colonial empire in one compact piece and of giving up other possessions, the variety of the political and economic needs of the German Empire shows us that a Colonial Empire essentially African could not suffice us. Africa is the nearest colonial territory, but the great future before China requires the maintenance and acquisition of strategic points in the Indian Ocean and the pacific.

Those upper ranks of the government therefore called for the internationalisation of Shanghai and Canton and the annexation of the European concessions in Tianjin and Hankou.

Finally, we come to the ideas of Wilhelm Solf, the head of the Colonial Ministry and therefore the one who would have to administer whatever Germany actually got out of the war. His case is interesting in two ways. First, his program barely changed from 1914 to 1918; second, he was basically alone in all of the German government in not wanting as much expansion as possible. Instead, he always advocated for a peace of understanding with England, based on a settlement in the colonies. Again, though, he especially meant Africa with that, so Asia is more of an afterthought, but it’s the idea that counts.

Another group of people for whom Asia was very much not an afterthought was the people who actually lived there – though, of course, they had lots of other people who readily spoke in their name. Qingdao was occupied by the Japanese, as was Micronesia. In New Guinea, the local population was quite fond of German rule when questioned by the Australian occupying force; this may have had something to do with the Australian reintroduction of flogging. A similar situation could be found in Nauru. The people of Samoa pressured New Zealand to reintroduce the public education system that the Germans had introduced and the New Zealanders had abolished, though after 1919, the dissatisfaction with the new administration also spread to other areas (the influenza pandemic of that year played a big role).

In all of those cases, however, three things have to be remembered. First, these were all colonies, and their inhabitants did not freely choose to be ruled by foreigners. In the words of Hiery, the best case was always a "marriage of convenience". Second, it was not that the people of New Guinea or Samoa were fond of German rule because it was German, but because of the ties of trust established with individual colonial administrators that were lost when those administrators were replaced by New Zealanders, Japanese or Australians. And third, that a fond remembrance of some past rule could be a useful foil to protest misdeeds and push for improvement of a current one.

In summary, Asia always played third fiddle in terms of German war aims to Europe and Africa; the plans for Asia constantly kept changing, though the return of the occupied current colonies was a constant (apart from Qingdao); and the population of those areas, while never consulted formally, did in some cases use positive examples set by the German colonial administration to push for an improvement of their successors.

Sources:

Bernard, Augustin: “Germany’s Colonial Aims”, in: Journal of the Royal African Society 16 (1917), pp. 306-313 (Mainly a translation of that article in the Deutsche Kolonial-Zeitung).

Fischer, Fritz: Germany’s Aims in the First World War, New York 1967.

Hiery, Hermann Joseph: The Neglected War. The German South Pacific and the Influence of World War I, Honolulu 1995.