Amid talks with the two campaigns, the four Michigan Democrats said in a statement they were "focusing on the possibility of a state-run primary in early June which would not use any state funding." Rep. Carolyn Cheeks Kilpatrick, one of the Democratic participants, said a likely date is June 3.
"This option would require the passage of legislation by the state legislature, and we look forward to working with the members of the legislature in the coming days to see if this option can be made a reality," the Democrats said.
Other Michigan Democrats working on the plan were Democratic National Committee member Debbie Dingell, Sen. Carl Levin and United Auto Workers President Ron Gettelfinger.
To go forward, any plan would require the approval of the two campaigns, the Democratic National Committee, state party leaders and Gov. Jennifer Granholm, who is backing Clinton.
Michigan Democrats need to act quickly because the politically divided legislature will have to sign off on the deal and approve how to spend the privately raised funds for a new election. Members of the Democratic-controlled state House and Republican-controlled state Senate leave at the end of the month on their two-week spring break.
The contest must be held by June 10 for the results to count under DNC rules.
The national party punished Michigan and Florida for moving up their primaries before Feb. 5, stripping them of all their delegates. The two states have been struggling to come up with alternative plans to ensure their delegates are seated at the national convention this summer in Denver.
Michigan held its primary Jan. 15 and Florida voted Jan. 29. Clinton won both, although she was the only major candidate on the Michigan ballot.
Kilpatrick said although she is optimistic, Detroit City Clerk Janice Winfrey has expressed concern they may not have the time or manpower to pull it off. She said they are trying to work through those issues.
Florida Democrats said they will make a decision by Monday on whether to hold a dual mail-in and in-person re-vote. But the plan floated this week faces opposition from the state's Democratic congressional delegation, and Obama has also expressed concerns about security and accuracy of a mail-in vote organized so quickly. Democratic National Committee rules require the vote to be scheduled by June 10.