AP/Susan Walsh, File
Sen. Lindsey Graham (R-South Carolina).
Graham's personal life has been widely discussed since he launched his presidential campaign earlier this month. If elected, he would be the first lifetime bachelor in the White House since President James Buchanan in 1856.
Audio of Kirk's comments was published by the Huffington Post, which reported they were "caught on a live microphone."
"I've been joking with Lindsey," Kirk said. "Did you see that? He's going to have a rotating first lady. He's a bro with no ho."
In an email to Business Insider, Kirk's press secretary, Danielle Varallo, said the senator's "bro with no ho" comment "was a joke between friends."
Kirk's remark referenced a recent interview in which Graham said he knew multiple people who could perform the role of first lady for official functions if he was elected.
"Well, I've got a sister, she could play that role if necessary," Graham said. "I've got a lot of friends. We'll have a rotating first lady."