Tory rebels believe "up to" 20 MPs who voted with the Government on the Internal Market Bill on Monday night would consider supporting Sir Bob Neill's amendment, with backers insisting "momentum is on our side".
It is understood ministers may try to find a compromise with the group by potentially supporting the amendment if sufficient changes are made.
After 30 MPs abstained from voting on the controversial legislation, the Government could come close to losing its majority if the amendment gains further support.
Michael Gove hinted that a resolution could be found in the Commons during Monday night's reading of the Internal Market Bill when he said Sir Bob was "on to something", saying: "He made the point that we need to show that we are operating in a constructive spirit, and I agree."
Mr Gove urged MPs to "look calmly" at the legislation, which gives the Government the power to override key sections of the Withdrawal Agreement, before assessing the "various amendments that may be tabled" (watch the Bill being debated on Monday in the video below).
Sir Bob's amendment would impose a "parliamentary lock" on any changes to the Withdrawal Agreement and is signed by four Commons committee chairs and two former Cabinet ministers.
Veteran backbencher Sir Roger Gale, one of two Conservative MPs who voted against the Government on Monday night, predicted that others could rebel next week, saying: "I took a view that you fight this tooth and nail at every step. Others have quite clearly decided they want to hold their fire for Bob Neill's amendment. There is much to play for yet."
Former International Development Secretary Andrew Mitchell lent his support to the Bill but is expected to also back the Neill amendment.
He told BBC Radio 4's Today programme: "The proposition that we should march through the lobby as lawmakers and say that we are going to ignore and disavow a law that we have passed, to do with the rule of law – that is completely unacceptable."
Mr Mitchell admitted the proposals were "causing very considerable anxiety and worry" on the Government backbenches.
Tobias Ellwood, the defence select committee chairman, said: "There are many, many colleagues that want to support the Prime Minister and get Brexit across the line but wish to do so in a way that doesn't breach international law (see video below)."
One supporter of changing the Bill suggested that the former Chancellor Sajid Javid was unlikely to be the only Tory "big beast" to express discomfort with the legislation in the coming days. Mr Javid said he would "regretfully" be unable to support the Bill and abstained.
On Monday night, MPs voted through the Bill by 340 to 263, a comfortable majority of 77. A total of 30 Tory MPs abstained but some, such as Theresa May, had prior engagements and did not attend the vote.
Mr Javid and ex-Attorney Generals Sir Geoffrey Cox and Jeremy Wright were among the most high-profile Conservatives abstainers.
Government sources claimed Robert Buckland, the Justice Secretary, asked for additional Cabinet scrutiny of a controversial clause in the legislation before supporting it.
On Tuesday morning Rehman Chishti, who resigned from his role in Government over the Bill, added his name to the Neill amendment. The outgoing special envoy said the amendment would "ensure full parliamentary scrutiny" and sovereignty.
Sir Keir Starmer, the Labour leader, accused Boris Johnson of "trashing Britain's reputation abroad and making it harder for us to get the trade deal we all want". He told the TUC conference: "My message to the PM is simple: Get your priorities right. Get on with defeating this virus. And get the Brexit deal you promised."