At the same time, Illinois Attorney General Lisa Madigan says she will not throw her hat into the ring but will instead seek another term in her current office.
"She loves her job as attorney general. That's the first reason," Mary Morrissey, Madigan's political director told the Chicago Sun-Times.
Madigan, a Democrat, had been urged by party heavyweights, including Sen. Dick Durbin, D-Ill., and White House Chief of Staff Rahm Emanuel to run for either the Senate or governor.
Kirk, meanwhile, is considered the top contender for the GOP nomination. The Highland Park Republican has been able to fend off challenges for his seat in the 10th Congressional District.
Sources said Kirk committed to the race for Burris' seat once word got out that Madigan would not be a factor, Crain's Chicago Business reported.
The Sun-Times said Burris has been having difficulty raising money and may decide not to seek re-election. Burris came under scrutiny over allegations that he cozyed up to ousted Gov. Rod Blagojevich to be appointed to the Senate after Barrack Obama won the presidency.