Juppé, a party heavyweight, was called in to mediate a dispute between Jean-François Copé and François Fillon, rivals to lead the UMP, which has been without a leader since Nicholas Sarkozy lost the presidential elections in May.
Former prime minister Fillon and Copé, the UMP’s former secretary general, have been trading accusations of fraud, vote rigging and bad faith since last Sunday, when a tight leadership ballot declared Copé the winner with just 98 votes.
The party electoral commission has since said that ballots cast in France's overseas territories that were not counted would have reversed the result, supporting claims from Fillon's loyalists.
However, the Copé camp claimed he would have won by a clear margin but for vote-rigging in the Mediterranean city of Nice.
Juppé, Copé and Fillon are set to meet at a secret location on Sunday night to settle the rift.
But Juppé appeared to carry little hopes of finding an amicable solution.
“If they don’t accept [my conditions], I don’t have any power to force them to. I am doing everything I can to succeed, even if I have very little chance,” he said.
The UMP’s former secretary general, Xavier Bertrand, wished Juppé “success” while highlighting that “the UMP has never been in so much danger”.
A meeting of UMP officials aimed at resolving ballot disputes collapsed on Sunday, with Fillon representatives walking out after about an hour.
A lawyer for the Copé camp accused them of "choosing to desert" the talks.
French media have spent the past week covering, analysing and commenting on the result, with some suggesting the dispute could pave the way for Sarkozy’s political return.
One of Sarkozy's close aides told the news agency AFP that the former President has been speaking with Juppé ahead of the meeting, and is "open to any initiative that could solve the situation."
Fillon is seen as more politically centrist, whereas Copé is more right-wing, having championed Sarkozy-era policies such as the ban on burqas.
The leader of the French far-right, Marine Le Pen, said on Sunday a new leadership ballot is needed to resolve the issue once and for all.
A survey published by Le Journal du Dimanche found 71 percent of people, including 67 percent of UMP supporters, would prefer a fresh election.
Another survey published by Le Parisien found 30 percent of people believed Fillon is best placed to face against François Hollande, compared with 19 percent of people who prefer Copé.