The chief executive of Peterborough City Council could take on the same job for the Cambridgeshire County Council.
Gillian Beasley might job share with the county council as it seeks to replace its outgoing chief Mark Lloyd who is moving to the Local Government Association.
The county council has approached Ms Beasley to take over on a temporary basis but a permanent job share appears to be on the cards.
City council leader Councillor John Holdich confirmed that Ms Beasley, who is paid £170,000 a year in her current post, could job share with the county council.
Speaking on BBC Radio Cambridgeshire he said he thought Ms Beasley should take the post if she thought she could cope with the extra work.
He also gave a 100 per cent assurance that the city council would not join with the county council once again having previously split from it to become an independent authority.
Cllr Holdich said: “I’ve always said it was ‘okay you’ve got to do it’ but it’s up to you personally if you want to do it as it’s an awful strain on her.
“The decision is close. I’ve just been talking to Gillian about this. If you think it works let’s do it, but let’s put notice periods in.”
Cllr Holdich said Ms Beasley will not be leaving the city council and will not receive an increase in salary, with the county council paying half her wage.
A spokesman for the county council said: “The county council is considering a range of options and nothing has been ruled in or out at this stage.
“It should be noted that the option of recruiting a new chief executive has not been ruled out either. We have approached Peterborough City Council to consider sharing a chief executive on a temporary basis as one possible option.
“No decision has been made, but both authorities are exploring the practicalities of how such an arrangement might work.
“A decision on the role of the council’s most senior manager can only be made by a meeting of the Full Council which could happen this October.”
The city council has been contacted about the story but has not yet issued a response.