South Yorkshire's forthcoming mayoral election should be shelved and an interim mayor appointed until a 'Wider Yorkshire' devolution deal can be agreed, council bosses say.
Barnsley and Doncaster Council want the government to postpone the election due to take place in May.
They say it will save £2m and allow time to agree an alternative deal.
The government said it was not possible to pass the parliamentary order needed to postpone the election in time.
Details of the proposal emerged as MPs were taking part in a debate on the future of devolution in Westminster Hall.
The request to postpone the election is contained in a letter to Communities Secretary Sajid Javid and regional MPs from Barnsley Council leader Sir Steve Houghton and Mayor of Doncaster Ros Jones.
It follows a community poll in the two towns in which people voted overwhelmingly against the Sheffield City Region deal.
Mr Javid has previously stated that he would be willing to allow Barnsley and Doncaster to join a Wider Yorkshire deal but not until 2022.
However, in the letter they say "this is too long for Yorkshire and Doncaster to wait, particularly in the context of Brexit" and that a "Yorkshire Mayor could be realistically elected in 2020".
They add that the interim arrangements will also be backed by Rotherham Council, which until now had stood alongside Sheffield City Council in opposing a Wider Yorkshire deal.
Analysis by James Vincent, BBC Look North political editor
Doncaster and Barnsley reckon they've already bent the will of the government, now they are trying to break it.
After getting the result they wanted in their community poll, the towns were offered a way to get the whole Yorkshire devolution deal they wanted - all they had to do was sort out the original devolution deal the government wanted first.
But it's not a good enough offer for them and the "route map" Doncaster and Barnsley have sent the government today might be better termed a list of demands.
They want a Yorkshire mayor by 2020 and an interim, unelected, mayor until then.
And if those are the demands, it's Sheffield who are the hostages. Doncaster and Barnsley say Rotherham has now joined them, leaving the Steel City outside looking in.
Although no official decision was made during the debate, Jake Berry, Northern Powerhouse minister, said the government did not intend to undo legislation to change the date set for the election.
Dan Jarvis, MP for Barnsley Central, said Mr Berry's reaction was a "little bit under ambitious", adding: "I think that where there would be a political will to make the changes, it would be entirely possible to do so."
To date the only devolution deal agreed with government would see the Sheffield City Region handed control of transport, strategic planning and skills as well as £900m of funding over 30 years.
However, the future of that deal was thrown in to doubt in September when Barnsley and Doncaster voted against progressing with it and gave their support to the Wider Yorkshire proposal.