Reid, in an interview Wednesday on MSNBC, told Rachel Maddow he and the Oklahoma Republican have met and "it's all over with," The Hill reported.
Coburn addressed the New York Young Republican Club on Monday, the New York Daily News reported.
"There's no comity with Harry Reid," Coburn told the group. "I think he's an absolute a--hole."
Reid told Maddow he's sure Coburn "didn't mean it."
Coburn and Reid have something of a history. Last year, Coburn apologized after publicly calling Reid "incompetent and incapable" and said more recently Reid is a "failure" who has been "dishonest" with him.