Updated 2:14 p.m. | Twenty-four hours after Sen. Carl Levin, D-Mich., announced his retirement, we  know more about who is not running to replace him than who is.

Former Michigan GOP Chairman Saul Anuzis said he is mulling a run and has been approached about about seeking the seat. “I haven’t had a chance to look at it,” he said in a phone interview.

But while Anuzis is keeping his name in the mix, there are many more Republicans taking their names out of contention, including Rep. Candice S. Miller, who announced Friday that she will not run.

“While I am grateful for the interest people have shown, I will not be a candidate for the U.S. Senate in 2014,” the chairwoman of the House Administration Committee said in a statement, according to The Detroit News. “It is my sincere honor to serve the people of Michigan’s 10th District in the United States House of Representatives and in 2014 it is my intention to seek their support for re-election.”

The paper reported that Cornerstone Schools founder Clark Durant and former state Attorney General Mike Cox will not run for Senate either. In addition, The Associated Press reported that Lt. Gov. Brian Calley has ruled out a run. State Attorney General Bill Schuette has also said he will not run.

While open Senate seats in Michigan are rare, both parties have a somewhat limited bench. The top tier of possible contenders includes Reps. Mike Rogers and Justin Amash on the GOP side. As for Democrats, the most mentioned name is Rep. Gary Peters, followed by former Rep. Mark Schauer.