The Tennessee republican said on "Squawk Box" he's "in the mix" for the job, but said others closer to the campaign are also interested. "Sure we've had some conversations with them," he said.
Former New York Mayor Rudy Giuliani, who unsuccessfully ran for the GOP presidential nomination in 2008, is rumored as the leading candidate for secretary of state in Trump's incoming administration.
At a Monday night event in Washington sponsored by The Wall Street Journal, Giuliani said that he "won't be attorney general," perhaps seen as a more natural role for the ex-federal prosecutor.
Corker had been mentioned over the summer as a possible Trump vice presidential choice. Trump ended up choosing Indiana Gov. Mike Pence as his running mate.
Addressing the reported turbulence in Trump's transition team, Corker said some turmoil would be expected when considering how tough it is to form a new government, especially for a businessman who's new to politics.
Pence, who served six terms in Congress, is well-suited to lead the process, he said.
— AP contributed to this report.