Hello! Japanese military leaders expanded the scope of their military operations in December 1941 (troops had already been fighting in China since 1937) thinking that war with the United States was inevitable. Although different commanders disagreed on strategy, it seems the general aim was to force the Americans to sue for peace after Japan had established hegemony and an "invincible" defensive perimeter over the areas of the "Greater East Asia Co-Prosperity Sphere." Nevertheless, I am not exactly sure how Japanese leadership envisioned postwar relations with the United States--yet given their failure to formulate a viable long-term strategy for victory against the Allies, perhaps they did not think much about the issue at all. I need to consult some books to give you a more detailed answer, but I'm away from home for the next few weeks.

There is an odd footnote to this, which I came across quite recently and might as well mention for the sake of interest. Sometime in December 1941, the Army Ministry's Research Section outlined goals for the eventual occupation and administration of a much more grandly conceived "East Asia"; this included Australia, New Zealand, and parts of the Americas. According to the "Land Disposal Plan in the Greater East Asia Co-Prosperity Sphere," an "Alaska Government-General" would have encompassed Alaska, Yukon Province ("and the land between that Province and the Mackenzie River"), Alberta, British Columbia, and Washington State. There would also be "Government-General of Central America" incorporating large swathes of Central and South America as well as the Caribbean, though "[t]he future of Trinidad, British and Dutch Guiana and British and French possessions in the Leeward Islands [is] to be decided by agreement between Japan and Germany after the war." Moreover: "In the event of her declaring war on Japan, Mexico [is] to cede territory east of Long. 95° 30’. Should Peru join in the war against Japan, it must cede territory north of Lat. 10°; and if Chile enters the war it shall cede the nitre zone north of Lat. 24°." The Army apparently believed that these conquests would be made some twenty years after the end of the Pacific War (which Japan would win, of course), and these territories would presumably be exploited in the same manner as the other constituents of the Co-Prosperity Sphere. You can find this document reproduced and briefly discussed in Richard Storry's The Double Patriots: A Study of Japanese Nationalism (Boston: Houghton Mifflin, 1957), 276 and Appendix II, 317-9.

Despite its provenance, I have not come across any evidence so far that this "Land Disposal Plan" ever received widespread acceptance or consideration in Japanese political and military circles (though I would like to do more research on the topic). I'm sorry I can't provide a more meaningful response! :(