Paul Blomfield, MP for Sheffield Central and a member of the Business Innovation and Skills Committee, made the comments last night at a fringe event during Labour's conference in Manchester.
Labour's current policy is to lower the fee cap from £9,000 to £6,000 if it were in power today - leaving the door open to establish a new policy for the 2015 general election manifesto.
Shabana Mahmood, the shadow higher education minister, who was also part of the panel at the Million+ and National Union of Students event, said that "on the specifics of a fees and funding policy...I don't take any option off the table".
She added that over-payment by the wealthiest graduates envisaged in Labour's current policy "does, in its detail, move us towards a more graduate tax-type system".
Mr Blomfield told the event - titled "Why a new higher education funding system is a matter of fiscal credibility" - that Labour needed to approach the funding issue with "humility" having introduced fees in 1998 and then legislated for top-up fees in 2004, despite a commitment in its 2001 manifesto not to do so.
He said a new funding system should be based on three principles: "that all those who benefit from higher education should make a contribution"; that there should be "no burden of debt"; and that "there should be no market in fees".
Mr Blomfield said if a market was established it would "only widen" and there would be "pressure" from within and outside the sector to lift the fee cap higher.
"We know the consequences of that. It will not only damage the sector but it will close routes to those students and those families who can't face the prospect of much higher fees for much more expensive courses in much more select universities," he said.
He added he was "encouraged" by past statements from Labour leader Ed Miliband and shadow chancellor Ed Balls in favour of a graduate tax. "I think that's the trajectory on which we should be moving," he said.
He noted obstacles such as the "misplaced" concern "of some universities about a fee-based system somehow enshrining a bogus autonomy. All of those issues are resolvable if we have the political will and decide on the trajectory of policy, which in my view should be a graduate tax."
Mr Blomfield's comments came ahead of Mr Miliband's keynote speech, in which he is expected to say that Labour should focus more on the 50 per cent of people who do not go to university.