"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.
Mark Brewer, chairman of the Michigan Democratic Party, said the potential privately funded primary was "a good first step" toward seating the state's delegation at the Democratic National Convention.
The agreement now hinges on getting the campaigns and party officials to approve legislation, still being written, that would set the primary for early June. In the statement, Brewer said party leaders would need to write legislation "that is acceptable to the MDP and both the Clinton and Obama campaigns."
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. Brewer said a revised delegate plan would also need to be approved by the state party's executive committee and the DNC's rules and bylaws committee.
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.
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.
Separately, Democratic Sen. Bill Nelson, who backs Clinton, has suggested one options - seating all the Florida delegates already chosen but only giving them half a vote each. Nelson discussed this idea with Clinton and Obama on the Senate floor Thursday, according to an aide, but no commitments were made.
Based on the Jan. 29 results, Clinton would have won 105, Obama 67 amd John Edwards 13. Instead they would get half those delegate votes.
Florida DNC member Jon Ausman on Friday filed an appeal to the rules committee asking that the state's 23 superdelegates and half its at-large delegates be restored. He argued that party rules say superdelegates "shall" be seated and that the punishment for holding an early primary is losing half the at-large delegates.
"They far exceeded their authority by giving us the death penalty," Ausman said.
While party rules at the time the primary date was moved did say that states would lose half their delegates, the rules committee later voted to strip Florida of all its delegates. Florida had 210 delegates, including 185 pledged delegates.
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.
Both campaigns said they would evaluate the plans. Obama spokesman Bill Burton said the campaign hoped "a resolution can be arrived at that is fair and practical."
Former Michigan Gov. James Blanchard, the co-chairman of Clinton's Michigan campaign, said they were "looking at this with great interest ... it has some great possibilities."
--- Associated Press Writers Brendan Farrington in Tallahassee, Fla., and Nedra Pickler in Washington and Kathy Barks Hoffman in Lansing, Mich., contributed to this report.
