Clinton won primaries in both states and if the delegates votes were to be counted she could receive a boost to her election bid.
But she faces an uphill battle, with the Democrat's 30-member rules and by-laws committee panel to win her demand that delegations be seated at the convention in Denver later this year with full voting rights.
'Every vote counts'
Clinton signed a pledge along with the other candidates not to campaign in either state, and Barack Obama, the Democratic frontrunner, took his name off the Michigan ballot.
After winning both contests, Clinton began to press for the results to be recognised.
Obama has said he is willing to compromise in hopes of unifying the party and moving on to the general election campaign against John McCain, the Republican candidate.
The panel will hear challenges from Florida seeking to seat half of the pledged convention delegates and all of the state's superdelegates.
A challenge from Michigan asks the panel to give 69 pledged delegates to Clinton and 59 to Obama.
Democratic National Committee lawyers sent an advisory memo to the committee suggesting it was within its rights to strip the states of their delegates and taking issue with Clinton's plan to seat the delegations.
The committee, which has 13 Clinton supporters on it, is free to arrive at its own solution.
Members have said they want to be fair to both campaigns and mindful of the need to follow party rules to prevent a mad rush of states to hold contests earlier and earlier in the process.
Even if the delegates from Michigan and Florida are reinstated, it is likely that Clinton will still lag more than 100 delegates behind Obama with the nomination in the hands of less than 200 undecided superdelegates.
Rob Reynolds, Al Jazeera's senior Washington correspondent, said: "There is a lot of discussion of rather arcane by-laws, the language of the party rules.
"Really this is the last chance for Clinton to try to deflect Obama's seemingly inexorable march towards the Democratic nomination.
"If the delegates do what Clinton would like them to do ... she will still not have enough delegates to win the party nomination outright.
"But she will have moved closer to Obama and she believes she will be in a better position to woo those important superdelegates."
Reynolds said that as a compromise the committee could punish Michigan and Florida by taking away half of their delegates.
They would then work out a formula by which the states could divide the delegates between Clinton and Obama.