The government is currently accepting ideas from local authorities "for how they wish to develop garden cities" and "how they wish to make use of the existing central government funding and support" as part of its garden city prospectus.
Currently, Ebbsfleet in Kent has been the only new garden city announced by the government.
But Nick Clegg said at the Liberal Democrat conference this week that a proposed rail line between Oxford to Cambridge would pass through locations where "a lot of the new garden cities need to be established".
He said: "We think that at least three major garden cities could be constructed along that route. Tens of thousands of new houses. But crucially, homes built in a properly planned and sustainable way."
Cherwell District Council said that Bicester, which would sit along the proposed East-West Rail Link, is designated as a growth area in its local plan, and that the council is now "currently reviewing the requirements for a bid" to become a garden city.
Barry Wood, leader of Cherwell District Council, said: "Bicester has many of the qualities required and already promotes many of the garden city principles which could lead to a Bicester Garden Town."
Work on the Bicester scheme is already underway. The development was one of the last government’s eco-towns.