Rep. Luis Gutierrez (D-Ill.) is under consideration by Gov. Rod Blagojevich (D) to replace President-elect Barack Obama in the Senate, an Illinois Democratic operative confirmed on Wednesday.

According to the source, the governor “has discussed the prospect” with the eight-term Chicago lawmaker, and the two Democrats “will talk more in a few days” about the possibly of his being named to the job.

Blagojevich’s office did not return a message left Wednesday morning to confirm the negotiations.

But in a statement, Gutierrez said his “priority isn’t being in the House or being in the Senate.”

“My priority is immigration reform,” he said. “Wherever I feel I can be most effective is where I want to be.”

Rep. Jesse Jackson Jr. (D-Ill.), who some had considered until recently the frontrunner to replace Obama, “has not had a direct conversation with the governor” about the seat, his office confirmed.

On Sunday, Obama formally resigned his seat, which Blagojevich will fill. Two weeks ago, the embattled governor formed a panel to help him vet possible Obama replacements.

“We’re obviously willing and waiting for the opportunity to sit down with the governor when he calls,” Jackson spokesman Ken Edmonds said.