Labour will call on Prime Minister Theresa May to make a series of changes including allowing parliament to replicate any new European Union laws on employment rights, the environment and consumer protection, The Times reported, citing a letter sent by Labour's Brexit spokesman to minister David Davis.
Offering an olive branch to defuse the revolt, Mrs May said she will "listen very carefully" to MPs' concerns - a big hint she will bring in changes.
MPs return to the commons next week and will move quickly into debates and votes on the crucial Repeal Bill, on which pro-Remain Conservatives will wield significant influence given Theresa May's slim majority.
In an August 31 debate, the main opposition Labour Party is planning to propose several changes to the repeal bill with a view to keeping Britain in the single market and customs union during a Brexit transition period after 2019, according to The Times.
A decision to vote against the bill was taken collectively by the shadow cabinet after Keir Starmer, the shadow Brexit secretary, set out the case against backing it.
The party said it could not support the bill in its current form because it would "let government ministers grab powers from parliament to slash people's rights at work and reduce protection for consumers and the environment".
Labour said last week that it wanted to keep Britain in the Single Market during a transition period after Britain's membership in the bloc ends in March 2019 - an alternative to the Conservative Government's stance.
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"The slogan of the Leave campaign was about people taking back control and restoring powers to Parliament".
Ministers appealed for unity ahead of the second reading of the EU (Withdrawal) Bill, with one senior figure warning Tory MPs that derailing the measure could open the door to power for Jeremy Corbyn.
A handful of Labour rebels could vote with the government, but the Scottish National party and Liberal Democrats also plan to vote against the bill after tabling amendments setting out their reasons for opposing it. And the bank has just predicted that, due to Tory in-fighting over Brexit, May's government will face a "no confidence" vote in parliament.
A Conservative backbench rebellion is growing over "Henry VII powers" granted to ministers in it that allow them to modify huge chunks of European Union law without MPs' scrutiny.
Pro-European Tory MPs have warned that they are preparing to rebel over the timetable for debating legislation, known as the programme motion, in a vote on Monday.
Some Labour MPs claimed their leader avoided both Brexit and immigration because his party's own position is ambiguous and is also split on immigration.
Chris Leslie, a Labour MP and former shadow chancellor, said: "Maastricht took five weeks to debate".