The Government remains on course for an awkward clash with its own MPs over plans to part-privatise the Royal Mail.
It has rejected a compromise to the proposal despite a Commons motion opposing part-privatisation being signed by 148 Labour members of Parliament.
The Compass think tank put forward a suggestion to turn the postal service into a not-for-profit company, in a similar model to Network Rail, rather than selling off at least a third to an overseas competitor.
Neal Lawson, director of Compass, said he had held "very constructive" talks with officials in Downing Street and the Business Department, warning that the Government would not be able to win support in the Commons for its Bill without Conservative support.
But Post Office Minister Pat McFadden told Sky News no deal had been done and that a "political fix" was not the solution to the Royal Mails problems.
"The Prime Minister's office said last night that the proposals published by the pressure group were not workable and not under consideration so I think this is an attempt by somebody to get some publicity," he said.
"The plan we have put forward is threefold: bring in a new investor; take away the pension fund deficit from the company; change the regulation to put Royal Mail on a level playing field with competitors.
"If alternatives and options are made they must be convincing in terms of their ability to transform the company, they cannot be a political fix which pretty much leaves Royal Mail where it is, because that would not be good for Royal Mail and it would not be good for the public."
Billy Hayes, general secretary of the Communication Workers Union, said: "The Government says it is happy to discuss alternatives for the Royal Mail, but when presented with a well-argued public model they immediately dismissed it.
"This is not a game of a political fix, it is about the future of our postal service which we all rely on - just look at the delivery of the swine flu leaflet.
"The Government must listen to the public and its own MPs."