Treasury Minister Simon Clarke and Northern Powerhouse Minister Jake Berry will meet the leaders of Leeds, Bradford, Calderdale, Kirklees and Wakefield Councils as part of what is described as a "devolution dash" across Yorkshire this week.
Talks are also being held with leaders in the East Riding and Hull, the Sheffield City Region and North Yorkshire and York so they can begin to catch-up with the powers held by mayoral authorities in Manchester, Liverpool and the Tees Valley.
The deal being discussed in West Yorkshire would see the county take control of extra powers and funding from Westminster, giving them more responsibility over local services. Such a deal failed to get government support in 2015 and last year Ministers rejected a 'One Yorkshire' arrangement which would have seen a metro mayor set up for the whole region.
Exchequer Secretary Mr Clarke said: “We are determined to level-up opportunities so that all communities, including those here in West Yorkshire, get their fair share of our future prosperity.
“Today we take a step forward by opening talks on a mayoral devolution deal for the Leeds City Region – right in the heart of the Northern Powerhouse. This will give local people, who know their area best, the power to shape their own destiny.”
West Yorkshire Leaders said in a joint statement: “We go into these discussions determined to secure a devolution agreement that meaningfully transfers powers and money from Whitehall to the Leeds City Region and helps us accelerate our work to deliver growth that benefits all our communities.
“We welcome the positive tone the Government has struck ahead of this meeting, including on the important role of collaboration at a Yorkshire level, and hope they will match the scale of ambition we have for this deal.
“We are ready to work quickly to secure an agreement which ensures the City Region is in the best possible position to improve the quality of life of our communities in the years to come.”
Northern Powerhouse Minister Mr Berry said: “This government is absolutely committed to transferring power, money and responsibility from Whitehall and putting it back in the hands of the people.
“Our discussions with West Yorkshire represent a significant step forward in securing a workable devolution deal that will allow local people to reap the rewards of having a powerful, locally-elected mayor.”
It is understood that West Yorkshire leaders will not just accept any deal offered for a transfer of powers and resources from Whitehall and will be seeking an agreement which delivers on local priorities.
They also want the funding made available as part of any deal to reflect the fact that other areas of the country such as Greater Manchester and the Tees Valley have had devolution for longer.