(CNN) - A proposal is taking shape for Michigan Democrats to hold a new presidential primary, a Democratic source close to the negotiations says, after the national Democratic Party refused to recognize the results of their first vote two months ago.
Under the proposal, the state of Michigan would hold a new primary on June 3, and the Democratic Party would reimburse the state for the cost of running the election, ensuring the state had the cash in hand before voting began.
The Democratic National Committee refused to recognize the results of the primary Michigan held on Jan. 15 because it allowed only four states – not including Michigan – to hold primaries before Feb. 5.
Many Democratic presidential contenders had their names taken off Michigan's ballot after the DNC decision, including Sen. Barack Obama. Sen. Hillary Clinton did not remove her name from the ballot, and won 55 percent of the vote. Some 40 percent of Michigan Democrats filed ballots declaring themselves "uncommitted."
The Michigan state legislature would have to push the plan through by next Thursday
Michigan voters wanting to cast ballots in the new primary would have to identify themselves as Democrats and certify that they did not vote in the state's Republican primary in January. Michigan normally does not require party identification in primary elections.
South Dakota is also slated to hold its Democratic primary June 3.
– CNN's John Roberts