Tory leaders in councils where the party could form a majority with Reform UK have said they are open to reaching an agreement to govern alongside the rival party.
New polling suggests that several councils will end up in no overall control after the local elections in May, forcing parties to consider confidence and supply arrangements.
This means that a party with a minority is supported by a rival that agrees to vote with it on key decisions.
Glenn Bluff, the vice-chairman of the Doncaster Conservative Federation said and agreement was "certainly possible."
He said: “There will be a bit of a power vacuum because I think Labour will not have the seats for a majority.
"You’ll end up in a situation where inevitably you’re going to need some kind of confidence support between Reform and the Conservatives.”