South and West Yorkshire would both control some tax and spending if local councils devolve powers to new combined authorities run by a mayor.
Under the proposals, strategic planning, transport and economic regeneration powers would be handed over.
The Chancellor, George Osborne, could announce the plan on Wednesday.
The five West Yorkshire councils - Bradford, Calderdale, Kirklees, Leeds and Wakefield - joined the neighbouring City of York in North Yorkshire to form a combined authority six months ago.
Barnsley, Doncaster, Rotherham and Sheffield councils have created a similar South Yorkshire body.
The existing councils would continue to run services such as education and waste management individually.
Under the current agreement one of the council leaders is chosen by the others to chair the combined authority.
The chancellor's idea takes this on much further with extra powers for the combined authority to control social welfare policy, raise tax and control public spending. In return leadership would be given to a new generation of "metro mayors" wielding considerable executive powers.
Councillor Peter Box, Labour leader of Wakefield City Council and current chair of the West Yorkshire Combined Authority, said he would welcome any extra power and budgets but totally reject a regional executive mayor.
Wakefield, Bradford, Leeds and Sheffield all rejected individual city mayors in referendums just two years ago.
"Just a couple of weeks ago the Deputy Prime Minister Nick Clegg was in Leeds and told us that we could have the devolved powers without having to accept an executive mayor," said Mr Box.
"Go on any street and it becomes clear the public will simply not accept another elected politician."
Andrew Carter, leader of the opposition Conservative Group on Leeds City Council, voted against creating a local executive mayor in the 2012 referendums.
"But, a metro mayor is a completely different proposition," he said.
Support for the idea has come from two of Bradford's MPs.
Gerry Sutcliffe, Labour MP for Bradford South, who was leader of the city council before being elected to parliament, says West Yorkshire has to follow the Manchester lead or it will see potential investment and economic growth being sucked over to the other side of the Pennines.
George Galloway, Respect MP for Bradford West, said he believed that West Yorkshire could reap the same benefits that have resulted from the strong leadership of London's mayors.
"We have had two now, both of them bigger-than-life figures, who have clearly made a difference to London," he said.
The individual councils would not enter into a formal merger. A similar arrangement has been announced for Greater Manchester's 10 councils.
"I am a great believer in the power of our cities to be big forces in the world," Mr Osborne said as he signed the deal with the Greater Manchester councils in November.
"Great cities like Manchester don't quite have a strong enough voice. And I want to improve that. I think you do that by having a directly elected mayor. I think that has worked in London".

The 48-year-old will work under new director of cricket Jimmy Adams and chairman of selectors Courtney Browne, both former Windies internationals.
Law had previously coached Sri Lanka and Bangladesh's national sides.
"I am excited at the opportunity to contribute to what I think is an interesting time for West Indies," said Law, who takes over on 15 February.
"I think this assignment has come at an important time of my career."
West Indies had been without a full-time head coach since Phil Simmons was sacked in September.
Having also had time in charge of Bangladesh Premier League side Khulna Titans, Law becomes the third Australian to coach the Windies after Bennett King (2004-07) and John Dyson (2007-09).
While he only played one Test in 1995 - scoring 54 not out in his only innings - Law appeared in 54 one-day internationals between 1994 and 1999, and was a losing finalist in the 1996 World Cup.
As well as captaining Queensland to their first Sheffield Shield win in 1994-95, he was one of the leading batsmen in English county cricket in long stints with Essex and Lancashire, as well as having a brief spell at Derbyshire at the end of his career.
Parts of Yorkshire could be run by a London-style directly-elected mayor if new plans are proposed in the government's Autumn Statement.
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West Indies have appointed former Australia batsman Stuart Law as their new coach on a two-year contract.