Support from members of the majority party means that Applebaum could have a shot at succeeding former mayor Gérald Tremblay's, should he have the backing of the opposition parties.
Yesterday, Applebaum said he was considering running for interim mayor as an independent councillor.
He also urged other party leaders to consider forming a coalition to run the city until the November 2013 election.
City councillor and the executive committee's vice-chair, Alan DeSousa, said Applebaum's coalition would be unstable. He said he thinks Applebaum is willing to cut a deal with anyone in order to be mayor of Montreal.
"In my opinion, it's a naked grab for power — high risk, high stakes roll of the dice," DeSousa said.
But Applebaum has stressed the importance of limiting the interim mayor's role, saying that the interim mayor should not be running for mayor of Montreal in 2013.
Applebaum was the chair of the city's executive committee before he resigned last week over citing a dispute with other members over whether to release an internal working document that had been suppressed by the committee.
He says he is best suited to head the proposed coalition.
"I'm in serious reflection [over] Union Montréal and my political future in that party," Applebaum told reporters on Tuesday.
Applebaum said he met with the leader of Vision Montréal, Louise Harel, and leader of Projet Montréal, Richard Bergeron, over the weekend to discuss his proposal.
He said his calls and texts to Union Montréal leader Richard Deschamps have not been returned.
He warned that if Deschamps does not sit down with him to discuss the idea of a coalition, Union Montréal could go from being the party in power to being excluded from a coalition executive committee.
Harel told reporters Tuesday she thought Applebaum's proposal for a coalition executive committee is interesting.
She added that Vision Montréal may still introduce its own candidate in the race for the role of interim mayor.
Union Montréal has named Richard Deschamps as its candidate for interim mayor.
Members of city council have until 4:30 p.m. tomorrow to submit their candidacy for interim mayor.
City council will vote on an interim mayor on Friday.