There were those who advocated just that in the US;
There were those who advocated just that in the US; however, it was in the 1850s, not the 1890s. Matthew Perry suggested the US should essentially annex the Ryukyus and the Volcano (Bonin) islands, among other territories.
And the US was involved in the various "Western" expeditions against Japan in the 1860s (Shimonoseki, for example); the issue there is that any overseas claims bring up the issue of representation in Congress, and how that impacts the balance between slave and free states in the 1850s, and US attention is almost entirely domestic in the 1860s.
In the 1860s, the various factions within Japan brought in foreign advisors and mercenaries from Britain, France, and the US; after the 1870-71 Franco-German war, the French were no longer seen in the same way, and so the British influences on the IJN and the German influences on the IJA came into play as a way to balance the two and modernize the Japanese armed forces.
There were similar patterns in other modernizing nations at the same time - South America being the most obvious...
By the 1890s, the Anglo-Japanese and German-Japanese connections were established; the Anglo-Japanese naval alliance developed out of their shared issues with European naval powers' potential expansion in Northeast Asia, first the Russians and then, after 1905, the Germans.
The political need for a Japanese-American alliance were not there.
Best,