Kenneth Clarke today said he had never before seen a need for a British Bill of Rights.
But the Justice Secretary told MPs and peers he now had an "open mind" and was waiting for the expert views of the commission which has been set up by David Cameron to consider the issue.
The Conservative Party is committed to scrapping the Human Rights Act and replacing it with a British Bill of Rights and the Prime Minister has come under pressure from some of his MPs to take action on the issue.
Mr Cameron launched the commission earlier this year to consider the case for a British Bill of Rights to replace the Human Rights Act, which currently enshrines the European Convention on Human Rights in UK law.
Mr Clarke said: "I've never been a supporter... I've never seen a need for a Bill of Rights myself in the past, but I now genuinely have an open mind.
"I have every respect for the people we've asked to advise us... and I wait to see what they will come back and recommend."
Giving evidence to the Joint Committee on Human Rights (JCHR), Mr Clarke said: "On the face of it, you could have a Bill of Rights which really restated the rights in the convention and was then adhered to by the British courts.
"That in theory wouldn't change anything from where we are at the moment.
"Once it gets debated, then there are people who obviously wish to have different features in the Bill of Rights and use it as a basis for reform of the way in which we implement our obligations.
"But I think there's no point in anticipating the advice."
Asked by the committee's chairman, Labour MP Dr Hywel Francis, if he still thought any Bill of Rights would essentially be a "Human Rights Act plus", Mr Clarke said: "It really is that I am waiting for the advice of the commission now.
"The reason we set up a commission is that there were obviously a range of views inside the Government as to the best way of proceeding.
"From left to right actually, there are both supporters and opponents of a Bill of Rights.
"So we've asked this expert commission, who again represent a range of views, to give us their expert opinion."
Earlier, Mr Clarke said the most important aim during the UK's chairmanship of the Council of Europe was to reform the European Court of Human Rights.
But he said there was "no intention whatsoever of weakening the court", adding the UK wanted to strengthen it by implementing reforms which would see it operate "properly as an international court, not an appeals court".
"I'm sometimes accused of being slightly off-message myself," he said.
"I'm not one of those who rigidly adheres always to doing what I should do, which is reading out the line to take.
"But on this occasion I've always stuck impeccably to the policy of the Government and I see not the slightest prospect of this Government having any other policy in the foreseeable future."