“We’ve moved closer on some points. That the [Swiss] government wants to privilege Swiss employees on the job market is OK for me if it takes in the framework of mutual recognition”, he said, referring to the "mutual" pact that governed EU-Swiss relations. “This will be possible without a doubt”.

The talks come after Switzerland, in a referendum in 2014, rejected EU free movement putting in jeopardy the country’s access to the single market.

A parliament panel later rejected the idea of imposing unilateral quotas on EU workers, with the lower house, on Wednesday to look at the job “privilege” proposal for Swiss residents instead.

Juncker did not give further details on what the deal would look like.

But he said he was “more optimistic” than in recent weeks and that the talks were moving in “the right direction” on what he called a “Swiss-specific arrangement”.

He noted that, during the Swiss negotiations, “we have Britain in mind, because these questions are interlinked”. He also said that Brexit was “another element adding to the difficult issues we have to discuss with our Swiss friends”.

The UK, which is expected to start talks on the terms of its EU exit next year, has said it wanted a “unique” deal that would allow it to impose immigration controls while keeping access to the EU market.

But most EU politicians, including Juncker himself, have so far insisted on full access for EU workers in return for the market perks for fear of creating a precedent for other eurosceptic member states.

Meanwhile, Switzerland's Schneider-Ammann also sounded a positive note on EU relations on Monday, saying: “We need a solution that both sides can say ‘Yes’ to. I’m confident that we can do it”.

He added that he was concerned that Swiss firms and institutes would lose access to the EU’s Horizon 2020 scientific research grants if there was no accord.