Kirk, who now holds the Senate seat previously held by Obama, has recently been involved in negotiations with Sen. Tom Coburn (R-Okla.) and Democratic Sens. Charles Schumer (N.Y.) and Joe Manchin (W.Va.) over a compromise on gun background check legislation.
The call comes as Obama reaches out to a number of Republican lawmakers in the House and Senate. Obama hosted a closed-door dinner with a dozen Republican senators a week earlier. The discussion at the dinner focused on the budget and deficit reduction, according to senators who were at the dinner.
Kirk was not one of the senators at the dinner.
Obama is also set to meet separately with the Democratic and Republican caucuses in the House and Senate throughout the week.