MPs may be given the chance to vote on keeping the United Kingdom inside the single market.
Pro-EU Conservative MP Stephen Hammond revealed on Wednesday he would table amendments to the Trade Bill which would propose the UK join the European Free Trade Association (EFTA).
EFTA membership allows membership of the the European Economic Area (EEA) and subsequently access to the EU single market. Iceland, Liechtenstein and Norway are EFTA members in the EEA.
Theresa May has ruled out EFTA membership as it would require the UK to accept EU freedom of movement rules.
The prime minister has said she believes cutting immigration was the driving factor in the referendum result.
But the so-called Noway option of EFTA is the preferred Brexit of many Tory MPs who argue it will soften the economic damage.
Hammond, a former transport secretary, staged a parliamentary debate today on EFTA membership.
The Wimbledon MP said while the referendum result made it clear the UK should leave the EU - it did not set out how.
“One of the great myths of that referendum was this country also voted to leave the single market and customs union, it didn’t,” he said.
“How we leave the European Union is the most difficult challenge facing this country, and it is up to us, the Parliament of this country, to decide how we do it.”
Hammond said the benefit of EFTA’s 27 free trade agreements covering 38 countries and 900 million customers should not be underestimated.
“Joining EFTA would be a significant help when it comes to making up for the loss of EU free trade agreements. It would demonstrate to the world that the United Kingdom is not leaving Europe as it leaves the EU,” he added.
Anna Soubry, one of the most ardently pro-Remain Tory MPs, has said she believes there is a majority in the Commons for EFTA membership.
Speaking in a Commons debate last week she said it was one of the ways to avoid a total “Brexit nightmare” for the economy.
Brexit minister Robin Walker rejected EFTA as he said it would not voters “direct control over decisions” in their lives.
Shadow Brexit minister Matthew Pennycook said EFTA membership was not Labour’s “first preference” but added it should “not be taken off the table”,