Doris Leuthard said officials from both sides will explore the issue of foreign judges to see if a compromise can be found – an exercise that is likely to pique the interest of British ministers.
Bern is currently attempting to negotiate a brand new framework for economic cooperation with Brussels to replace its existing one against a backdrop of widespread opposition to further integration.
Switzerland is a partial member of the Single Market through a complex and dated web over over 100 separate Free Trade Agreements, granting it sector by sector access to the EU.
But the European side in particular is unhappy with this archaic arrangement and wants to agree a new form of partnership which would tie the country closer to Brussels in the future.
The current FTAs, dating back to the 1970s, are not governed in any way by the European Court of Justice although the country does accept the rules of the club and free movement of people.
Keeping free of the jurisdiction of euro judges is a key red line for a number of politicians including MPs from the anti-EU Swiss People’s Party (SVP), the biggest in parliament.
Unlike the other three non-EU members of the Single Market – Norway, Liechtenstein and Iceland – Switzerland is not signed up to the EEA agreement and the Efta court.
This means its trading relationship does not update itself with the EU automatically and many Swiss firms have subsidiaries in EEA countries, particularly Liechtenstein, to improve their market access.
Ms Leuthard met with the EU Commission president Jean-Claude Juncker earlier today to discuss the progress towards a new deal, with the latter saying things were “going in the right direction”.
At a press conference afterwards she said the foreign judges issue remained a tricky one but elusively added: “We found some flexibility here and will go into this in more depth in the months ahead.”
In a bid to move the process along Switzerland has agreed to contribute another £1 billion in “cohesion payments” to the EU budget over 10 years as a sign of solidarity.
The negotiations will be keenly watched in London, where British officials will be keeping an eye out for any concessions Brussels is prepared to offer Bern in return for accepting more EU laws.
And similarly Swiss politicians are keeping very close tabs on the ongoing Brexit negotiations for the same reason, in the hope that elements of a deal granted to the much larger UK can be applied to their new pact.
Mr Juncker today insisted that he is determined to keep the two negotiations separate, but the parallels between them are such that what happens in one set of talks could easily affect the other.
Switzerland’s relationship with Brussels hit the buffers in 2014 when the country’s population voted to curb free movement and impose quotas for EU nationals – something that would have invalidated its Single Market access.
However, last year MPs in the parliament managed to circumvent the tricky referendum vote by agreeing a system with the EU whereby people registered as unemployed in Switzerland are given first crack at open jobs.