Liverpool and Everton are to meet UK Sports Minister Richard Caborn next week for talks about sharing a stadium.
Liverpool have advanced plans for a new stadium and have previously denied they were interested in sharing it.
But Caborn is behind the idea of a groundshare and may briung his influence to bear.
A Department of Culture, Media and Sport spokesman said: “Mr Caborn has had a request to convene a meeting.”
“He is more than willing to talk through the issues. He is generally behind the concept of ground-sharing and has supported the recent agreement between Leicester City and Leicester Tigers.”
Caborn could influence the North West Regional Development Agency (NWDA), which could provide some funds for a joint venture.
The cost of Liverpool’s proposed new 60,000-seat stadium has risen from an original £80m to more than £100m, according to reports.
But Rick Parry, the club’s chief executive, has said his club had no interest in ground sharing.
Liverpool spokesman Ian Cotton added: “We have asked the North West Development Agency to consider our grant application on the basis of our single club use of a new stadium. This is a point we have made repeatedly to the NWDA.
“This application isn’t just about a new stadium. It is about a project which will act as a major catalyst for the regeneration of the whole of North Liverpool.
“It will bring proven benefits to the whole of the local community and it is time there were signs of real progress on delivering these.”
And Liverpool manager Rafael Benitez has ispoken out against a groundshare.
“Talk of two teams sharing a stadium always causes problems and in my view it would not work,” the Spaniard told his club’s website.
“It would not be good for the pitch, because obviously there would be double the amount of games played on it, and it would not be good for the supporters of Liverpool or Everton.
“Both are teams with lots of supporters and each have their own identity. By sharing a stadium with their rival team they would lose that.
“If the only option is to share then fair enough but it is better to have your own stadium. I know from my time in Spain that groundsharing is not popular.
“In Madrid you have Real and Atletico, in Valencia you have Valencia and Levante, in Barcelona you have Barca and Espanyol, and in Sevilla you have Sevilla and Betis. They all have their own stadiums. That is what the supporters want.
“True, Inter and AC share a stadium in Milan, but look at their pitch. It is not good. Also, in terms of atmosphere it is better that a team plays in its own stadium.
“In five years time we hope to be playing good football in our own new stadium.”
Everton, who shelved plans for a new stadium of their own, appear to be interested in the minister’s proposal.
However, given their parlous financial position, they are unlikely to be able to share all the costs of any new development, and may find themselves in the humiliating position of becoming minority partners and de facto tenants of their arch-rivals.
Keith Wyness, the Everton chief executive, told the Liverpool Echo newspaper on Friday: “It is another one in a series of meetings related to that subject.
“We will be attending with an open mind to listen to any ideas that are put forward.”