"Obama basically apologized for us" on the world stage, and Americans are "tired of apologizing," Sternlicht told CNBC's "Squawk Box."
Trump has tapped into a "deep vein," the desire of the United States to win, said Sternlicht.
"Right from the start with 'Make America Great Again,'" the presumptive GOP presidential nominee's campaign slogan was on the mark, he said. "We love winning."
The chairman and CEO of the $53 billion investment firm Starwood Capital Group said Trump and Democratic front-runner Hillary Clinton are both capable leaders.
Sternlicht, who said he knows both candidates, said he could support either of them if they move to the center.
"[But] the standard deviation on both candidates is pretty high," said Sternlicht, acknowledging that Trump has been pushed way right and Clinton way left. Sternlicht said the general election will be won by the candidate who is able to capture middle-of-the- road voters.
Trump was able to be "all over the place" during the Republican primaries and caucuses, but he must now define himself, said Sternlicht, who describes himself as a fiscally conservative and socially liberal independent voter.
How Trump may evolve has been a major theme among GOP leaders who have been reticent of supporting him.
After Trump met on Thursday with House Speaker Paul Ryan, a joint statement read: "We will be having additional discussions, but remain confident there's a great opportunity to unify our party and win this fall."
Ryan, who said last week he was "not ready" to support Trump, said following the 45-minute meeting with the billionaire real estate mogul was "very warm and genuine." But Ryan did not endorse Trump.