Conservative remainer MPs have a “role to play” in building a coalition to drive a soft Brexit through the Commons, Nicola Sturgeon has said as opposition parties seek to find common ground with unhappy Tory backbenchers.

In comments which gave the first indication of a Labour-SNP alliance, the Scottish National party leader suggested opposition parties would look at the Norway model, proposed by senior Tory backbenchers including former ministers Nick Boles, Nicky Morgan and George Freeman.

The Scottish first minister stressed that there was some way to go until they collectively decided which option to agree on, with a second referendum and membership of the customs union and single market all still “on the table”.

The Guardian understands that SNP MPs, along with Labour and the Liberal Democrats, have been talking to their Tory remainer counterparts with the aim of voting down Theresa May’s plan and reaching agreement around an alternative.

“In terms of the softer remain element of the Conservatives, I think they have a role to play in putting that majority together,” Sturgeon told reporters after meeting Jeremy Corbyn and Vince Cable in the wake of last week’s Brexit chaos. She also met the prime minister.

Key Tory remainers, thought to be backed by the cabinet Brexiter Michael Gove, favour a Norway-style arrangement – temporary membership of the European Free Trade Association or the European Economic Area – until a trade relationship is agreed.

Boles, who is the main proponent, has now suggested this could become permanent if the EFTA/EEA relationship evolved to address concerns about free movement and rule-taking.

Sturgeon said: “If that’s moving towards a permanent single market, customs union, that’s what the SNP has been arguing for for the last two years and that’s one of the options that potentially we can build a majority around. It’s not the only option, but it’s one of them, and the more options we’ve got on the table right now the better.”

Boles, who believes his plan would come into play once all other options had been voted down by the Commons, told the Guardian: “I’ve had conversations with opposition MPs. They’ve been clear that it’s something they could imagine becoming a point of discussion, but not if it’s explicitly temporary.”

Sturgeon also hinted that the SNP, which has 35 MPs, could back a second referendum. “The option that would stop Brexit is another vote and Labour’s official position is not for that at the moment, but hopefully, over the course of the next few weeks as these discussions develop, we’ll see movement on all sorts of positions.”

However, she cautioned against over-optimism. “Let’s take this step by step. There’s no doubt this is the job we’ve got to do – saying that you’re against the prime minister’s deal and that we all think that no deal is not an option are important statements, but they only take you so far.

“We’re not there yet … We know what we don’t agree with and don’t like. What we now need to do is work together on what we think is the better alternative. I’m up for the SNP being part of it.”

The party has some clear differences with Labour on Brexit, particularly over free movement, as well as the Lib Dems, who have been pushing for a second referendum. Sturgeon said they may not end up “on the same page” but “we’ve got to look ahead now … and I feel a responsibility to have a go on that. The important thing now is that we focus on where we think we can build majorities.”

A Labour spokesman said Corbyn had had a constructive meeting with Sturgeon. “They discussed their common opposition to Theresa May’s botched Brexit deal and determination to work across parliament to prevent a disastrous no-deal outcome.”