ATHENS—The U.S. military is in talks to expand its operations in Greece, including using more air and naval bases here, signaling a potential move toward the eastern Mediterranean amid growing tensions with Turkey, officials said.

There are both geopolitical and geographical factors that make Greece an appealing site for the U.S. military, the officials said. Politically, U.S.-Greek relations are at an apex and both nations have concerns about their North Atlantic Treaty Organization partner, Turkey, U.S. officials said. Geographically,...