The field of potential GOP candidates for the open Senate in Michigan is shrinking rapidly.

Michigan Attorney General Bill Schuette (R), Rep. Candice Miller (R), former attorney general Mike Cox (R) and 2012 GOP Senate candidate Clark Durant have all said they will not run, as have former state party chairwoman Betsy DeVos and her husband, former GOP gubernatorial nominee Dick DeVos.

"Carl Levin has had a distinguished and honorable career in the United States Senate," Schuette wrote on his Facebook page. "I wish him all the best in his future endeavors. As for myself, I've got plans to keep working as your Attorney General for six more years."

That's not a flat-out no, but it certainly suggests that Schuette won't be in the race for the seat being vacated by veteran Sen. Carl Levin (D). Some Republicans in the state are still hoping that a "Draft Schuette" movement would bring him into the race and clear the field.

The Detroit News reported that Miller, Cox and Durant have also passed on the race. Of the three, Miller was seen as perhaps the most formidable candidate.

DeVos adviser Greg McNeilly told Post Politics that "neither one are considering a run for Senate, however they’re both passionately committed to getting a Republican elected to that seat."

Both Republicans and Democrats have pretty thin benches in Michigan, despite the state's size. But Democrats appear likely to get their choice candidate, Rep. Gary Peters.

On the GOP side, Reps. Mike Rogers, Dave Camp and Justin Amash remain potential candidates. Another former state party chair, Saul Anuzis, is not ruling out a bid.

Perhaps the most intriguing name to be floated so far, though, is Scott Romney, the older brother of Mitt, who has been making calls about the race, according a Michigan GOP strategist.

Scott Romney, 71, ran for attorney general in 1998 but lost at the GOP convention.

Updated at 5:04 p.m.