The government is in the final stages of negotiations over a European Court ruling that it must allow prisoners the right to vote.
The European Court of Human Rights has ruled that a blanket ban on voting for anyone sent to jail is illegal.
The government has until the end of November to decide how to react.
The UK has been on a collision course with the European Court of Human Rights (ECHR) since the Strasbourg court ruled in 2005 that it was a breach of human rights to deny prisoners a vote.
The court ruled it was up to individual countries to decide which prisoners should be denied the right to vote from jail, but said a total ban was illegal.
In May of this year, it gave the UK six months to outline how it proposed to change the law on prisoner votes.
'Over my dead body'
At the time, David Cameron said it would make him "sick" to change that, and that he would resist the ECHR ruling, saying the ban on voting from jail "should be a matter for Parliament... and not a foreign court".
Downing Street sources said the prime minister still believed that "when people go to prison, they lose their right to vote".
The coalition has to decide whether to comply with the ruling, seek a further delay or do nothing and risk a fine or maybe more.
Of the report that prisoners could get the vote, a government source told the BBC: "It is completely untrue. It's not happening. It's complete nonsense."
They said the discussions were "legally complicated" but declined to elaborate further.
BBC political correspondent Robin Brant said one Tory backbench MP said any change would be made "over my dead body", and another that the justice secretary should get on with his day job and show the ECHR that "two can play at interminable delay".
Labour has previously said it would back the prime minister's stance.
But Liberal Democrat backbencher Stephen Williams, a member of the constitutional reform select committee, has said prisoners serving short sentences should be allowed to vote as part of their rehabilitation.
At present, the only prisoners allowed to vote in Britain are those on remand.