West Yorkshire Combined Authority (WYCA) is planning to bid for a share of a £4.2bn Government transport fund next year, so it can build the mass transit system by 2040.
In a report, WYCA said light-rail, tram-train and prioritised routes for electric buses are being considered and “one or more” of those modes of transport could be used.
It is exploring plans for a network, consisting of nine lines, that links towns and cities across West Yorkshire, including Leeds, Bradford, Halifax, Huddersfield and Wakefield.
“We recognise that Leeds is the biggest city in Europe without its own mass transit system. That can't be right,” said Mr Shapps.
"I know there have been two or three attempts in Leeds previously to get this going and they've sort of ended up being very controversial and haven't quite got there.
"But we're very, very keen to work with both Leeds and now the new West Yorkshire Combined Authority Mayor (Tracy Brabin) to kickstart that project. We're very, very keen to see it done.
"Obviously, Leeds and the wider region itself need to work hard to work out what kind of transit system that it wants, because the previous couple of attempts have not worked out.”
According to a recent report, WYCA want to see construction begin in "mid 2020" and ensure it is completed by 2040.
Ms Brabin said: “’I’m pleased to hear that Grant Shapps stands ready to make sure that West Yorkshire finally gets the mass transit system it deserves.
“Better transport is key to revitalising our villages, towns and cities, tackling the climate emergency and giving our communities improved access to jobs, skills and opportunities.”
She added: “Turning our vision for West Yorkshire mass transit into a reality will require long term funding certainty from the Government.
“The devolution deal signed between West Yorkshire and Government on March 11 in 2020 set out a commitment from Government to collaborate with us to develop a West Yorkshire mass transit system.
“We look forward to working with Government to shape the proposals and welcome funding decisions from Government which would accelerate its delivery. I hope to hear from Grant Shapps soon to discuss this further.”
Plans for Leeds Supertram were abandoned by the Government in 2005 before a highly controversial bid to bring a £250m trolley bus network to the city was scrapped in 2016.
Almost 30 years and £72m of taxpayers’ money were spent on these failed schemes.
But shortly after the 2019 General Election, Prime Minister Boris Johnson said his newly-elected Government will "remedy the scandal that Leeds should be the largest city in Western Europe without light rail or a metro”.