Yes, some Americans and the European powers thought that the Treaty of Paris, in which Spain ceded Cuba, Puerto Rico, and the Philippines to the U.S., could be the beginning of a U.S. Empire. The European Empires were wary that America could join their club and power politics. Some American politicians, businessmen, and military personnel called for additional smaller possessions (such as islands) all over the world. Although there was lots of opposition to any of these new "territories" becoming proper U.S. states.

But that fear of or advocacy for American imperialism quickly subsided when the Philippine-American War began in 1899. As a gruesome guerilla war with heavy loss of life on both sides, it wasn't exactly popular (especially as it went on). McKinley and the Republicans were still able to win the 1900 election endorsing American "expansion", but after that new acquisitons wouldn't have been too popular any more. Even Theodore Roosevelt, an ardent imperialist, shied away from formal imperial adventures (except for Panama). In the following years, the U.S. continued to ensure its interests by ways of informal imperialism such as gunboat/dollar diplomacy, but a "bigger" America wasn't on the table any more.

This was a very condensed answer and I might have not answered your (a bit vague) question fully or in-depth. So if you have any follow-up questions, do ask. I'm happy to answer them.