A group of MPs is planning to force indicative votes in parliament on a series of Brexit options, including a second referendum and a softer departure, as several cabinet ministers suggested it could be the only way to resolve the political impasse.

If MPs vote down the possibility of a no-deal Brexit on Wednesday night, they will vote on Thursday on whether to seek an extension to article 50. Efforts are under way to persuade Theresa May to announce plans then to hold debates on Brexit options the following week in order to determine a new path for parliament during a short extension.

If May does not propose indicative votes herself, a coalition of MPs, including the Conservative Sir Oliver Letwin and Labour’s Stephen Kinnock, plan to force the votes by laying down an amendment on Thursday that would pave the way for legislation to ensure the votes took place.

The mechanism would be similar to that proposed by Letwin and Labour’s Yvette Cooper to prevent a no-deal Brexit, an amendment that gives time for a bill to ensure a vote on extending article 50. This time, that bill would legislate for indicative votes next week.

“Our plan is for a proper process and debate to determine what can command parliamentary support,” Kinnock said. “We hope that it is something that can be offered by the prime minister but if it is not, then the process we had for the Cooper-Letwin amendment shows we have the mechanism and the support to make it happen.

“We believe that indicative votes would show a cross-party consensus behind ‘common market 2.0’, which is picking up more and more cross-party support.”

The group’s plan is to devote next week in parliament to debates on different Brexit options, which could include a no-deal Brexit, a second referendum and the “common market 2.0” proposal for a Norway-style deal, spearheaded by Kinnock and the Conservative Nick Boles, and backed by other influential MPs, such as Labour’s Lucy Powell and the Tory Robert Halfon.

Votes would then take place the following week, on 25 and 26 of March, in the style of a “deferred division”, where MPs are able to vote on multiple options on a ballot paper. Proposers of the different options would be able to prepare short summaries of how they could be implemented and negotiated with the EU.

The environment secretary, Michael Gove, and the chancellor, Philip Hammond, both hinted on Wednesday that they expected indicative votes to be either proposed or forced next week.

Asked by the MP Emma Reynolds about indicative votes, Gove said in the Commons: “I think that, depending on how the house votes today, we may have an opportunity to vote on that proposition tomorrow. But one of the things that I think is important is that we, as quickly as we possibly can, find consensus.”

Hammond said that Thursday would be “an opportunity to start to map out a way forward towards building a consensus across this house for a deal we can collectively support to exit the EU in an orderly way”.

The idea has been encouraged by several other cabinet ministers, including the education secretary, Damian Hinds, and the business secretary, Greg Clark.

One cabinet source said they did not believe May had fully embraced the plan yet, but that her recognition on Tuesday that the house had, had given supporters hope she would allow the votes to take place.

After her deal was defeated, May said: “The EU will want to know what use we mean to make of such an extension [to article 50]. This house will have to answer that question. Does it wish to revoke article 50? Does it want to hold a second referendum? Or does it want to leave with a deal but not this deal?

“These are unenviable choices, but thanks to the decision the house has made this evening they must now be faced.”

Intensive talks are ongoing between Powell and Kinnock and the Labour leadership about securing frontbench backing for the common market 2.0 plan. It is unclear, however, if MPs that are strong supporters of a second referendum would support any plan for a soft Brexit.