Theresa May is considering a new plan to bring legislation to the House of Commons to allow MPs to thrash out a compromise Brexit deal among themselves, if talks with Labour fail to reach a consensus.

Numerous cabinet sources confirmed to the Guardian that a plan had been discussed to bring forward the withdrawal agreement bill, which could be a way to attempt to bypass a meaningful vote in parliament.

It is understood May and her team have gone cool on the idea of MPs having more indicative votes, which she had suggested would be binding if talks with Labour do not progress.

However, Labour is keener on bringing forward the withdrawal agreement bill to test support for amendments on various options. A Labour source said this had been discussed in the Cabinet Office on Tuesday, but ruled out frontbench support for the plan at this stage.

Three cabinet sources said the plan was very much on the table, with the bill potentially being brought forward within a week. However, others played down the idea, saying the government acknowledged it still did not have the numbers for the withdrawal bill to pass the Commons.

Under the plan, the government would hope to persuade the Labour frontbench to allow the bill, known in official circles as the WAB, to be used to ratify the Brexit deal and to give legal reassurances on workers’ rights, environmental protections and a “Boris lock” to prevent agreements being unpicked by a future Tory leader, such as Boris Johnson.

Some cabinet ministers believe the bill’s progress could act as an indicative votes process – cross-party groups of MPs would be able to amend it to bind the government into elements such as a customs union, which could then potentially gain a parliamentary majority.

After an amendment passed by Dominic Grieve in 2017, UK law requires a meaningful vote in parliament on the withdrawal agreement and political declaration – but supporters of the move believe the WAB could potentially be amended to remove that requirement.

Talks with Labour on a Brexit deal had more success on Tuesday, with an acknowledgement from the government that it was open to seeking changes to the political declaration, firmer guarantees on abiding by future EU regulations on workers’ rights and potentially changing some of the language around a customs union.

It is understood, however, that the fundamentals of the government’s position on the customs union have not changed and the two sides remain at some distance, meaning talks are likely to drag on into next week.

Labour also has serious concerns that May might not have the full authority of cabinet or her party to pursue such a deal and could not ultimately bind a hard Brexiter successor such as Johnson or Dominic Raab to any agreement.

The shadow Brexit secretary, Keir Starmer, raised the issue of Liam Fox, the international trade secretary, writing to Conservative MPs saying a customs union with the EU was the “worst of all worlds” as evidence that it does not look like the government is completely on board with negotiations.

Following the talks, Rebecca Long-Bailey, the shadow business secretary, said: “We’ve had really constructive discussions today and covered a number of issues in great detail. There’s not really been any fundamental shift or a change in position of the deal itself. But we’re hopeful that progress will be made. We’re continuing discussions with the government over the coming days.”