The government has denied that Theresa May plans to scrap the requirement for local areas to have an elected mayor in return for sweeping new powers from Whitehall.
It was reported on Monday that the prime minister was planning to water down the devolution deals drawn up by George Osborne when he was Chancellor.
Elections for the mayoralties of Greater Manchester, Liverpool and the West Midlands are due to go ahead next May.
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According to The Times, May is planning to amend the scheme so that future agreements would not hinge on an area having a directly-elected mayor as well.
But a spokesman for the Department for Communities and Local Government said: "Devolution deals will continue in the usual way. Elected mayors remain the best way to make them work."
The prime minister's spokeswoman said The Times story was "wrong", but admitted future devolution deals may not involve mayors.
She said: "We are taking this forward on a case-by-case basis, looking at what is right for the area. We continue to support devolution and the deals in place and support having strong, accountable governance, including mayors."
George Osborne was one of the leading advocates of metropolitan mayors to give more democratic accountability as groups of local authorities took over more powers from Whitehall.
Former deputy prime minister Lord Heseltine, a key advocate of devolution, said it was “inherently unlikely that the prime minister on holiday... is initiating policies of this sort from her mountaineering relaxation".
Speaking on the Today programme, he said: “Can we just put the thing in context? I think it was about a week ago we got The Times running a story about the end of the Northern Powerhouse. Again, I didn’t believe that and it turned out to be untrue; I think this will turn out to be untrue as well.”
Labour’s candidate for mayor of Liverpool Steve Rotherham said: “The prime minister gives the impression that the left hand doesn’t know what the right hand is doing.
“In October 2015 she voted in favour of devolving powers where electing regional mayors were part of the agreement. However, it now appears she is trying to row back the former chancellor’s flagship policy by indicating she is not comfortable relinquishing decision making from the Westminster elite."
He added there was “undoubtedly a fear” inside No 10 of the Labour party performing strongly in such elections.