The idea was floated by the Meiji Japan's first Minister of Education, Mori Arinori, Minister from 1885 till his death. He began working on the idea while being ambassador to the USA in Washington. His reasons, published in 1873 in Education in Japan, were as follows:

Without the aid of the Chinese, our language has never been taught or used for any purpose of communication. This shows its poverty. The march of modern civilization in Japan has already reached the heart of the nation－the English language following it suppresses the use of both Japanese and Chinese. The commercial power of the English-speaking race which now rules the world drives our people into some knowledge of their commercial ways and habits. The absolute necessity of mastering the English language is thus forced upon us. It is a requisite of the maintenance of our independence in the community of nations. Under the circumstances, our meagre language, which can never be of any use outside of our islands, is doomed to yield to the domination of the English tongue, especially when the power of steam and electricity shall have pervaded the land. Our intelligent race, eager in the pursuit of knowledge, cannot depend upon a weak and uncertain medium of communication in its endeavor to grasp the principal truths from the precious treasury of Western science and art and religion. The laws of state can never be preserved in the language of Japan. All reasons suggest its disuse.

Mori even wrote Yale professor William Dwight Whitney about the subject:

The spoken language of Japan being inadequate to the growing necessities of the people of that Empire, and too poor to be made, by a phonetic alphabet, sufficiently useful as a written language, the idea prevails among us that, if we would keep pace with the age, we must adopt a copious and expanding European language. The necessity for this arises mainly out of the fact that Japan is a commercial nation; and also that, if we do not adopt a language like that of the English, which is quite predominant in Asia, as well as elswhere in the commercial world, the progress of Japanese civilization is evidently impossible...

As ambassador and intellect, Mori must have needed to do a lot of translation, which would've made the shortcomings of the Japanese language at that point in time, since the language had not created or adopted technical vocabulary of the sciences and laws because only a small group of intellectuals would've had those knowledge in the Edo period, and they were taught and would've used Dutch. As well, opinion of China was fairly low among the powers. These short comings were recognized by other Japanese educators and intellectuals as well. However, none agreed with Mori's plan to adopt English.

For instance, immediately after Mori published his book arguing the point, Baba Tatsui, a young exchange student in England, published his own book in direct response to Mori, An Elementary Grammar of the Japanese Language with Easy Progressive Exercises. In the prefix, Baba notes:

We have two objects in publishing this bookthe first, to give a general idea of the Japanese language as it is spoken; and the second, to protest against a prevalent opinion entertained by many of our countrymen, as well as foreigners who take some interest in our country, and to show the reasons why we do so. It is affirmed that our language is so imperfect that we cannot establish a regular and systematical course of education by means of it; and that the best way is to exterminate the Japanese language altogether, and to substitute the English language for it. Those who maintain this opinion ought to have examined the language and proved its imperfection as a medium of intellectual thought and expression, but so far as we are aware they have not done so.
For example, Mr. Mori, in his introduction to “Education in Japan,” says, “without the aid of the Chinese, our language has never been taught or used for any purpose of communication. This shows its poverty.”
...
Although we admit, in some respects, that the Japanese language is imperfect, yet it seems to us that it is not so imperfect as it is represented to be.
...
We admit that in several respects the English is far superior to the Japanese, but at the same time, we think in many respects the latter excels the former.

Likewise, Shimizu Usaburō, fellow member of the Meirokusha intellectual society who wanted to abolish kanji (Chinese characters) and retain only the kana (Japanese alphabet), said in 1874 that the idea of replacing Japanese with English "is out of the question."

Professor Whitney was likewise strongly against the idea. In his reply to Mori, while he agreed with the ideas of advancing English education in Japan and writing Japanese with the English alphabet (now known as rōmaji, or "Roman letters") he stated:

But of the Japanese language itself I feel very unwilling to take a depreciatory view, or to accept any plan for the advancement of culture in Japan which does not include the ennobling and enriching of the native speech so that itself shall become a means of the increase of culture. Even with a fully-developed system of national instruction, it would take a very long time to teach a strange language to so large a part of the population as to raise the latter in general to a perceptibly higher level. If the masses are to be reached, it must be mainly through their own native speech.
...
Let the English language be studied as much as possible; let it take in Japan the place so long occupied by the Chinese; let it become the learned tongue, the classical language; let its treasures of expression be drawn upon as freely as circumstances shall admit and favor — but let the beneficial effect of all this be felt in the Japanese tongue itself; let the experiment be fairly and fully tried whether this is not capable of being raised and perfected, so as to be the worthy instrument of an advanced civilization. If the experiment fails at last, and the substitution which you propose has to be carried out, there will have been nothing lost, but much gained, in the mean time; the due and necessary preparation will have been made, and the substitution will take place by a more organic process, from below, instead of being violently imposed from above.

So Mori did put forth the idea. He in fact believed it so strongly that not only did he still publish Education in Japan which was completed after he received Whitney's response, he included Whitney's response in the book, but still pushed for the idea. And he did work hard to advance English education in Japan as its first Minister of Education. But when he proposed the idea, he was not Minister of Education, and no one supported replacing Japanese with English. When Baba published the second edition to his book in 1888, he noted the idea was dead. For all his work at modernizing Japan, Mori was assassinated in 1889. A month before his assassination, the Japan Weekly Mail notes that Mori "does not intend to carry into effect his supposed hobby of rendering English the national language of Japan."

Reference:
Joseph, J. E. (2011). "'The unilingual republic of the world': Reactions to the 1872 proposal to make English the national language of Japan." Revista Argentina de Historiografia Linguistica (Rahl), 3(1), 53-65. http://www.rahl.com.ar/Revistas/I%20-%202011/joseph-RAHL-(1)2011.pdf
山井徳行 (2004). "国語外国語化論の再考(1)森有礼の「国語英語化論」と志賀直哉の「国語フランス語化論」について." 名古屋女子大学紀要. 人文・社会編 50, 179-191.