The Conservative-run cabinet at Peterborough City Council could be threatened by a cross-party coalition.
Labour and Co-operative Councillor Ed Murphy is standing to be leader of the council and has received indications that he could be supported by other parties.
The challenge to the Conservatives follows last week’s elections where the party moved further away from a majority of seats and saw its leader Cllr Marco Cereste defeated.
After the election for 20 seats across 19 wards, the Conservatives were left with 26 councillors out of 56.
The remaining seats are held by: Labour (12), Independents (seven), Liberal Democrats (four), UKIP (four) and Liberals (three).
A decision on who will lead the council for the next four years will be voted on at full council on Wednesday.
The Conservatives have chosen Cllr John Holdich as their new leader, while Labour have chosen Cllr Mohammed Jamil as the head of their group.
Mr Murphy said he would stand if nominated by two members of the council and would fill the cabinet with people of all parties.
Cllr David Harrington, leader of the Peterborough Independent Forum, said: “I shall support a cross-party cabinet. I would consider backing Cllr Murphy as his past record shows he is a capable member.”
Cllr John Okonkowski from UKIP said his party would consider supporting the Conservatives but added: “UKIP are on our own and will back any party that’s right for Peterborough.”
Cllr Chris Ash from the Liberals said: “I think what the council needs is a leader that can work with all groups and be pragmatic and caring.”