Mr Redwood, who led the Tories' parliamentary opposition to the measure, is reviewing the party's stance on the Labour policy. The trade and industry spokesman has always been a fierce critic of the pounds 3.60 per hour minimum wage, condemning it as "bad for business" and forcing an all-night sitting in the Commons to debate its consequences.
But other senior party figures now accept it is "inconceivable" the Tories could fight the next general election with a pledge to scrap a policy that has benefited two million low-paid workers. A U-turn would also help the party's efforts to combat recent polls, which showed a deeply held public view that the Tories were "mean-spirited".
But given Mr Redwood's strident opposition to the policy, the Government would seize on any climbdown by the Tory party leadership. Mr Hague might therefore seek to minimise embarrassment by moving Mr Redwood to another frontbench post or sacking him altogether.
Archie Norman, who has announced he was standing down as the party's chief executive to prepare for a frontbench post, has also made clear that he would like to get the trade and industry portfolio. Mr Norman, who has built a high-profile business reputation as the chairman of the Asda supermarket chain, has been among those leading the calls for a change of position on the minimum wage.
But Mr Hague, who is still trying to heal the party's divisions over Europe, may fear that any move of Mr Redwood to a less influential job, or a decision to sack him, would leave him with a formidable enemy on the back benches.
Mr Redwood famously resigned as Welsh secretary from John Major's cabinet in June 1995 to fight for the party leadership. His outright Euro- scepticism, presently restrained through his position in the Shadow Cabinet, could serve to highlight the Conservatives' divisions over the issue in the run-up to the next general election.
Speculation over Redwood's position first surfaced earlier this year when there were several press reports suggesting he and Conservative spokes- man on foreign affairs, Michael Howard, were on their way out. At the time Mr Hague reassured the trade and industry spokesman that such speculation was untrue, but sources close to Mr Hague have made clear that the Tory leader has never completely trusted him.
It was, as insiders put it, "the trust issue" with Mr Redwood that stopped Mr Hague from promoting him to shadow Chancellor - a job Mr Redwood desperately wanted.
"If William Hague finally gets rid of John Redwood it will be the resolution of a battle that began back in '97. William was always wary that John was briefing against him and that he did not have his complete support," one insider said.