The pledge in the Tory manifesto is deeply unpopular with many Conservative backbenchers because it could see their seats disappear altogether.
And sources have said that the government does not want to risk a rebellion with a majority of just 12.
The plan was to equalise the size of constituencies to around 75,000 each with exemptions for Orkney and Shetland, and the Western Isles and reduce the number of seats to 600 to save money.
The proposal was part of the Coalition Agreement but was blocked by the Lib Dems after a Tory backbench rebellion prevented reform of the House of Lords.
It is expected that if it went ahead Scotland would lose at least another seven seats bringing it down to 52 in the Commons.
It is thought that the plans would also give the Conservatives an extra 20 seats in the next election.
However, whips have told some Tory backbenchers that while the government will push to equalise the size of constituencies they will drop the proposal to reduce the number by 50 to prevent a rebellion.
Claiming that assurances have been given on the number of constituencies, one backbencher said: “Turkeys won’t vote for Christmas and they [the whips] know it.”
Another joked: “They [the government] want to avoid blue-on-blue action”.