Nick Clegg, the deputy prime minister, is said to have won his cabinet fight to scrap control orders, the restrictive conditions that impose virtual house arrest on some terror suspects.
Under alternative measures awaiting government approval, suspects will no longer have to wear electronic tags or have a home curfew imposed on them, and will be allowed to use mobile phones and home computers for the first time, according to the Sunday Times.
They will also be allowed to travel wherever they want in Britain, but not abroad, it is claimed.
The report comes after a group of human rights organisations upped the pressure on the government over the issue.
However a spokesman for Nick Clegg told the Guardian that no decision had yet been made regarding control orders.
He said: "No decision has yet been made. The discussion has been ongoing in government."
The Liberal Democrats promised to scrap control orders as part of their election manifesto commitments, but the issue has caused wrangling within the coalition government, under pressure from the Home Office and MI5 to retain the controversial measures.
Jonathan Evans, the head of MI5, wrote to David Cameron, the prime minister, two months ago to say he could not guarantee that suspects currently under control orders would not resume planning attacks against Britain.
The measures are one of the most sensitive civil liberty issues for ministers as opposition of Labour's authoritarian counter-terror policy was seen as important to both parties in the coalition. In October, the Lib Dems wrote an open letter to Cameron warning him that any decision not to scrap them would jeopardise its civil liberty credentials.
The measures were introduced in 2005 after the US terror attacks to replace detention without trial of foreign suspects, which the House of Lords ruled breached human rights. They were aimed at suspected terrorist suspects who cannot be prosecuted because the evidence against them, either from informants or wire taps, would compromise intelligence sources.
Nine suspects are currently subject to control orders.
The Sunday Times reported that the cabinet was poised to approve an alternative deal in its first meeting of the year next week.