Analysis of the potential economic impacts of the service have suggested there should be a station in West Yorkshire between Leeds and Manchester and a further stop in York to serve the north and east of the region.
The West Yorkshire Combined Authority (WYCA) is now pressing Transport for the North, the body leading the project, to include the additional stops in its plans.
Concerns have been raised that the project, known as HS3 or Northern Powerhouse Rail, is focused too narrowly on cutting journey times between Sheffield, Leeds and Manchester.
The WYCA analysis found there would be “significant” economic benefits from an additional stop in West Yorkshire in addition to Leeds.
A report to be considered by the combined authority, made up of council leaders from West Yorkshire and York, this week says: “The evidence points to it being located in Bradford and in particular in Bradford city centre based on regeneration opportunities and benefits to the economy and the labour market.”
The report says there are “strong, positive regeneration impacts” that would result from a stop at York.
Further work has now been commissioned to look at options for both a Bradford city centre station or a “parkway type facility that could serve both Bradford and other centres”.
WYCA’s work has looked more widely at the implications of the Northern Powerhouse Rail project including ensuring that parts of the area not directly served are connected.
The report says there will need to be wider transport improvements alongside HS3 to ensure all areas benefit.
It also warns that it is vital other promises made on rail improvements, including the new rail franchises which started earlier this year, are not lost as a result of work on HS3.
And it points out the key role the design of stations on HS3 will have in making sure passengers can make “seamless” changes from one rail service to another or onto other forms of transport.
Earlier this year the Government’s National Infrastructure Commission recommended HS3 should be at the heart of a wider strategy to cut journey times in the North to boost the economy.
It called for an “integrated plan” for the development of HS3 to be in place by the end of next year.
The commission argued the initial focus should be cutting journey times between Manchester and Leeds, targeting the goal of 30 minutes between the two.
Then chancellor George Osborne subsequently promised £300m to take forward proposals to improve transport across the North including the development of the HS3 proposals.