Michael Howard, the Home Secretary, has made it clear to colleagues he would be willing to take over responsibility for Clegg's case, and he would be "very sympathetic''.
Although Clegg has been transferred to Wakefield prison, he remains under Northern Ireland jurisdiction.
In June 1993, at Belfast Crown Court, Clegg was convicted of murdering Karen Reilly,18, while she was a passenger in a stolen Vauxhall Astra driven by her friend, Martin Peake,17, at speed through an army checkpoint.
Clegg, now 26, was serving with the Parachute Regiment's 3rd Battalion when he, and other members of the 14-man army patrol, fired 36 shots at the car after warnings to stop were ignored. Martin Peake also died.
Last week the Law Lords rejected an appeal by Clegg, ruling that the use of force had been grossly disproportionate.
A statement by Sir Patrick Mayhew, Secretary of State for Northern Ireland, was put in the whips' office at the Commons last night to reassure Tory backbenchers that Clegg could be given early release. But government sources confirmed it would be a simpler to transfer Clegg's case to the jurisdiction of the Home Secretary. All Sir Patrick would have to do was apply to the Government for the change to be made, said a source.
Tory backbenchers demanded an emergency Commons debate on the Law Lords' rejection of Clegg's appeal. The request was made by Iain Duncan-Smith, the Tory MP for Chingford, but was turned down by the Speaker, Betty Boothroyd. Mr Duncan-Smith said: "It is an embarrassment for the Northern Ireland Office. Pte Clegg has become a pawn."
Yesterday, campaigners fighting for Clegg's release, said they now had new scientific evidence which could prove that he did not fire the lethal bullet.
The campaigners, who include present and former members of his regiment, believe Clegg acted in accordance with the Yellow Card outlining the circumstances in which troops are allowed to open fire in Ulster, and said that they intended to refer the case back to the Court of Appeal in Northern Ireland where they would try to prove that the round taken from Ms Reilly's body may not have been fired by Clegg after all.
At the time of the shooting the soldiers justified their action by claiming that one of the patrol, Pte Barry Aindow, had been hit by the car, and Clegg said that he had fired in self defence. But the court was told that the bruising on Pte Aindow's leg was caused by another soldier stamping on him to make it look as though he had been struck by the car.
The court accepted that three of the four bullets Clegg fired were justifiable because he thought the car was being driven at Pte Aindow, but convicted him because the fourth shot, which killed Ms Reilly, was fired when the vehicle had gone past the patrol.
Clegg, who has been in custody for more than three and a half years (including time he spent in army custody before the trial), is only the second British soldier to be found guilty of murder while on duty in Ulster.
Simon McKay, Clegg's solicitor, told a news conference at Nostell Priory, Wakefield, that the campaigners had new evidence which they hoped would prove that Clegg's conviction was both "unsafe and unsatisfactory''.
Irish bemused, page 2