According to The Times, Michael Gove has proposed abolishing English Votes for English Laws (Evel) – a Commons procedure introduced after the Scottish independence referendum.
Put to ministers last week, it would see the requirement that things affecting England are approved by only English MPs would be abolished.
Mr Gove said: “Ultimately, it’s a convention which arose out of a set of circumstances after the 2014 referendum, where you had a coalition government and so on.
“We’ve moved on now, so I think it’s right to review where we are on it.
“The more we can make the House of Commons and Westminster institutions work for every part of the UK and every party in the UK, the better.
“We have been throughout Covid operating without English Votes for English Laws.
“And I think that’s worked well, and I think that we can reflect on the lessons of operating without the need for English Votes for English Laws.
“But obviously it can’t just be a unilateral decision by any individual, it has to be accepted by the Commons as a whole.”
The SNP and Scottish Conservatives have long opposed the mechanism for creating “two tiers” of MPs, with Scottish Tory MPs having pushed for its abolition since 2017.
A Whitehall source added: “Abolishing Evel would reaffirm the principle that we are one United Kingdom, with a sovereign Parliament comprising members elected on a basis of equality, representing every community, able to make laws for the whole kingdom.”
Senior Tories, however, worry it could undermine the legitimacy of any government elected without a majority of English seats.
The proposals have already been opposed by two Cabinet ministers – Thérèse Coffey, work and pensions secretary, and Gavin Williamson, education secretary.
They are said to worry it would leave future governments vulnerable to English laws imposed against their will.
Scottish Secretary Alister Jack is also believed to support the plans and no other ministers have opposed them.
The plans were welcomed by Labour’s shadow Scotland secretary Ian Murray.
He said: “EVEL was an ill-judged and reckless act by David Cameron which undermined the Union just hours after Scots voted to remain in the UK.
“The policy is an incomprehensible mess which has weakened British democracy, weakened Scotland’s voice in Parliament, and created two classes of MPs despite being supported historically by SNP MPs.
“It led to the perverse situation where some unelected members of the House of Lords are more powerful than elected MPs. It was also never needed.
“Any move to scrap EVEL is welcome, but this saga shows that the Tories can’t be trusted to stand up for the Union.”
Mhairi Black MP, the SNP's shadow Scotland spokesperson, said: "Reports of scrapping English Votes for English Laws haven't appeared due to a sudden interest in non-English MP participation. It is yet another cheap political move by the Tory government to try and maintain the broken union – and it is doomed to fail.
"Far from being a partnership of equals, time and time again Scotland's voice in Westminster has been ignored.
"Scotland doesn't need constitutional tinkering – we need independence.”