In the wake of Gordon Brown's unshackling of the Bank of England, Ms Abbott's name is being increasingly mentioned for the prestigious post by people on both the left and centre-right of the party.
The theory is that the granting of independence to the Bank would have to be balanced by a Treasury committee showing much more teeth and one that keeps a sharp eye on the Governor, Eddie George.
One senior Labour source said: "Diane has been on the committee for seven years and in that time built up quite a formidable expertise. She should really have been moved on to the Shadow Treasury team, others with less experience have moved there. The feeling is that she deserves the committee chair, this will channel her natural aggression in a constructive way.
"Brian [Sedgemore] is also very good and impressive. He is the other natural choice as the chair. But he has not been as present at the committee as often as Diane, and anyway there is likely be another important role for him elsewhere."
Ms Abbott said yesterday: "Obviously, if given the opportunity, I would welcome the job. I worked closely with the Conservative members of the committee and got on well together."
The Tory election meltdown has resulted in the departure of all but two Tory members of the Treasury committee, including the chair, Barry Legg. In any event, Labour would now provide the majority of members and fill the chair.
Among the remaining members are the Tory MP Quentin Davies, the acerbic inquisitor of David Willetts, and Labour's Brian Sedgemore, who is also on the left of the party and a possible rival to Ms Abbott.Reuse content