Peter Skates, Cheshire East’s acting director of place, said devolution could bring financial benefits and increase local powers.
He told Cheshire East’s corporate policy committee on Thursday it was “timely and important” to hold talks with the government.
Labour figures said the talks did not commit the council to anything.
Sam Corcoran, the council leader, said Cheshire East had a “very close working between” with Cheshire West and Warrington, and said there was no risk of Cheshire East’s funding being “syphoned off”.
Labour members said devolution could instead mean better transport and more of a say in what happens locally.
Independent Wilmslow councillor Mark Goldsmith said shared the Conservatives’ concerns but would not know if they were valid unless there were talks with the government.
Seven councillors voted in favour of the council holding talks with government about devolution options, four voted against and one abstained.