"We've had conversations," the Tennessee Republican told CNBC's "Squawk Box," adding that "at the end of the day" he would support the party's nominee. Corker said he sees "a great deal of evolution taking place" with Trump.
"I thought the foreign policy speech was a step in the right direction," Corker said.
He was referring last month's foreign policy address, in which Trump rejected the terms of the nuclear deal with Iran, called for more investment in missile defense in Europe and accused the Obama administration of tepid support for Israel.
The Republican race has been run in reverse, said Corker.
"Instead of people being different on policy issues, it became somewhat of a personality campaign," he said. "Now we're going through that second phase, that usually is first, where I think there's a lot more focus on policy issues."
Addressing Republicans who said they refuse to support Trump, Corker said it's time "just to chill." He believes "a coming together taking place."
Trump arrived at GOP headquarters on Thursday to meet with House Speaker Paul Ryan about how to unite the splintered party. Corker said he expects the meeting to go well.
Corker said he has "no reason to believe" that he's being considered by Trump as a possible vice presidential running mate.