If agreed, the idea would see the Yorkshire stretch of HS2 built earlier and later connected to the rest of the line through the East Midlands to Birmingham and on to London.
The move would open up the possibility of fast services between Leeds and Sheffield beginning much sooner than currently planned.
But more significantly, the Yorkshire stretch could also form part of a proposed 125 mph transpennine rail link dramatically cutting journey times between Leeds, Sheffield and Manchester.
The proposal is expected to feature as part of a 15-year investment plan being put together for the Government by Transport for the North (TftN), a new body bringing together councils from Yorkshire, the North West and North-East to work with bodies such as Network Rail and the Highways Agency.
Other ideas on the table include running more trains on electrified lines, increasing motorway capacity by opening up hard shoulders and improving links to the North’s ports.
Leeds City Council leader Keith Wakefield said: “Making sure that there are better links between the northern cities is a policy we should all support.
“But it has got to be more than words. We want to see action, and one of the ways they could convince people, to demonstrate good faith, is starting HS2 earlier with the Leeds to Sheffield link.”
The Government set up TftN as part of its wider project to pool the strengths of the North’s towns and cities to create an economic “powerhouse” that can compete against the world’s major cities and make the UK less economically dependent on the South-East.
Transport Secretary Patrick McLoughlin met with TftN in Leeds yesterday to discuss its proposals before a formal report is published in March which will include costings for the high speed transpennine link.
Mr McLoughlin said there was still a lot of work to be done before the route of the second phase of HS2 from Birmingham to Leeds is confirmed.
He added: “I hear the eagerness to get it done quicker and if we can, I’m certainly up for it.”
The first phase of the HS2 project will see a new line built connecting London and Birmingham before phase two takes two lines further north with one heading to Manchester and the other to the East Midlands, Sheffield and Leeds.
On the current timetable, services on the new HS2 line to Leeds and Sheffield will begin around 2033 serving new stations at Sheffield Meadowhall and on Leeds’s south bank.
The Government will be told that building the Yorkshire stretch earlier would accelerate the economic benefits to the North sooner and help make the economic case for starting work on the new stations which could also serve the new high speed transpennine trains.
Manchester City Council leader Sir Richard Leese, who chaired yesterday’s meeting, said: “Once the parliamentary consents are in place then to start at the Leeds end as well as the Birmingham end would make perfect sense because you do it quicker and if you do it quicker then you get more cost reliability.
“Clearly we are adding another factor to this which is that by accelerating Leeds Sheffield bit gives them that potential for high speed connectivity not just to Manchester but to Manchester Airport.
“Actually from an economic point of view for Leeds and Sheffield its that Manchester Airport bit that’s probably the most important part of that.”