Well, the simple fact is that they did try. I apologize that I don't have the time to craft you a brand new, personalized response, but there are several I have written in the past which might be of interest, that I'll present with brief annotation.

So in the '30s, forcing Jewish emigration was the goal of the Nazi state, and much of the German Jewish population did in fact leave, at great personal expense due to the emigration tax levied on them, which is detailed more in the second post of this chain. Encouraging emigration to Palestine was one briefly explored solution, and at points, the Germans even explored options to do it all in one fell swoop, considering Madagascar as a place to make a giant Jewish "homeland", although serious consideration was quite brief. The drive to "the final solution" wasn't only ideological as some people are inclined to understand it, but also practical too - check out /u/commiespaceinvader speaking about the "Functionalist-Intentionalist" debate here which should explain this better. The German Jewish population was tiny compared to that further east, and with the capture of Poland and the Western USSR, Germany found itself with millions of Jews, and no way to expel them, since, you know, there was a war going on! As I touch on in the linked answers, the solution at this point was genocide. You can find a number of answers that go more in depth here in the FAQ too.

The policy of forced emigration of undesirables (which encompasses Jews mostly) was undertaken on a massive scale in pre-war Nazi Germany. The idea that the solution to the so called "Jewish Question" in Germany could be solved via emigration was done through intense pressure placed on the Jews living in Germany that created a climate so inhospitable that emigration seemed the only viable way to maintain their safety and livelihoods. Between 1933-39 over 250,000 Jews emigrated (legally and illegally) to countries all over the world, but mostly to neighbouring European countries, America, Palestine and Shangahi.

However, Jewish emigration was severely hampered in several ways. Firstly, it was extremely expensive to leave Germany, the Jews first being stripped of any foreign currency in 1934 during the devaluation crisis and the mass exodus of 37,000 wealthy Jews in 1933 caused the Reichsbank to place quotas on the amount of Jewish capital that could leave the country,as well as a large number of extra taxes and levies placed on the emigration process in line with policy of complete and utter exploitation of Jewish capital. This led to the second and third barrier, which were respectively the refusal of foreign nations to accept virtually penniless Jews from Germany, and a stagnation of emigration from Germany (20,000 per annum in 1938) due to the fact the only Jews remaining in Germany were devoid of any financial assests to secure visa's. Emigration stopped altogether with the war, and the focus switched from emigration to expulsion to Poland, or more specifically the General Goverment, which would eventually lead to the "Final Solution". I won't get in to this as I feel that's not the question asked but I'd be happy to elaborate.

Sources: "The Origins of the Final Solution" Christopher Browning

"The Wages of Destruction" Adam Tooze

Others have given more general answers, but I want to point out that in referring to deportations "from Germany" you're making a common mistake about where the Holocaust happened and who it targeted. The vast majority of victims were from occupied Eastern Europe, especially Poland, Ukraine, and Belarussia, not from Germany. Jews were only about 1% of the German population, and most German Jews were driven to flight before the policy of genocide was adopted. The Holocaust is better understood as an expedient wartime reaction to the "crisis" (by Nazi lights) of suddenly having significant numbers of Jews on hand as a result of rapid military victories, not as something that was carefully planned out long in advance.

Others have commented on the fact that the vast majority of the victims of the holocaust were not from Germany itself. But to answer your specific question of the local Jews, they did want to do just that (at least before the war). In fact the number of Jewish refugees leaving (or wanting to leave) Germany before the war was so high that in July 1938 an international conference (the Évian conference) was called by the U.S. to discuss the problem. Hitler is known to have said of the conference:

I can only hope and expect that the other world, which has such deep sympathy for these criminals [Jews], will at least be generous enough to convert this sympathy into practical aid. We, on our part, are ready to put all these criminals at the disposal of these countries, for all I care, even on luxury ships.

It does seem therefore that the final solution was at least at that point in time not necessarily imaged as genocide. However countries were not prepared to increase the refugee quotas (remember that anti-Jewish sentiment was widespread before WWII), and when the war broke out this level of cooperation between Germany at it's belligerents was out of the question.

Well, as Georgy_K_Zhukov said, they tried a few times. What I can add to what Georgy_K_Zhukov said is that there also was a conference named Evian Conference. This took place from 6-15 July, 1938, in France. 32 countries (ex. France, Belgium, Netherlands, Canada, Australia, Sweden, UK, US, Switzerland, Denmark..) gathered to talk about the Jewish immigrants. Not a lot of countries were prepared to open their borders to them. Correct me if i'm wrong but I think that the US agreed to take 300.000 Jews but it was gonna be a very slow process with complications. The UK claimed that they were full, France as well. The Netherlands accepted Jewish immigrants but said that the ones that were already in the country, should leave (Or in other words, the percentage of Jewish immigrants in the country could not change). Australia didn't want to take any because they were scared of the racism and discrimination that would follow. To conclude, not a lot of countries were open to the immigration of the Jewish population. As a last resort, in 1939, around 900 jewish citizens from Hamburg, Germany were able to board a boat named "MS St.Louis". The boat finally arrived at Cuba later on that year but were eventually denied entry to the country. So the boat left for Florida where they were also refused... They unfortunately were forced to go back to Germany where they would meet the same faith as the others... In response to Evian conference and the voyage of the St. Louis, Adolf Hitler gave a speech addressed to the world in which he said: "You don't want them? We will do you a favor and then take care of them", by that he meant that he would eventually start killing the Jewish population. Lastly, another famous story is the story of the boat named Stroma. In 1942, Nearly 800 Romanian Jewish refugees were on board. They were headed to Palestine to start their new lives but they needed to stop at Istanbul to receive their visas. Nearly no one received their visas and for the ones that got them, some complications followed. The Turkish government also said that no one was allowed access to the country. Eventually, the boat's engine failed and was unable to move so the Turkish police was forced to drag the boat away from the harbor and in open sea. The people were scared as their food began to ran out, and no hope was in sight (They wrote HELP US in English and in Hebrew). On Februar 24, 1942, a Russian submarine mistook the boat as an attack boat from the axis powers and sunk the boat. Nearly all passengers died of drowning, hypothermia or in various other ways. I hope this helped, it's my first time answering (I'm just a history buff).