Bern has been struggling to reach a deal with the European Union after Swiss voters last year approved immigration quotas, which goes against the freedom of movement of people accord and threatens other bilateral agreements.
The federal government had submitted a proposal to Jean-Claude Juncker, European Commission president, who has agreed to it, the NZZ am Sonntag newspaper reported online on Sunday, citing a reliable source.
The seven-person government is set to discuss the proposal this week, the weekly said.
Swiss secretary of state Mario Gattiker met last week with Richard Szostak, a negotiator for Juncker, the newspaper said.
The basis for an agreement on the immigration issue is an article of the free movement accord that states a joint committee with Swiss and EU representatives can adopt measures “in case of serious economic or social problems”.
Gattiker and Szostak have developed a model using this provision to allow the Swiss immigration initiative to be implemented, NZZ am Sonntag said.
This could be done without changing the free movement accord, which would require a unanimous decision of all EU member states, the newspaper said.
It cited a source saying that Juncker is interested in reaching an amicable agreement with Switzerland for two reasons.
The first, is the many cross-border workers living in the EU whose jobs in Switzerland would be at risk.
The second, is that Brussels wants to avoid Bern making a unilateral use of a "safeguard clause" in the free movement accord that would encourage the UK, which has itself being pushing for reforms on immigration, to follow that example.
There are still concerns in Switzerland because a resolution needs to be be reached quickly.
The initiative backed by Swiss voters calls for a change in the constitution on immigration restrictions that must be implemented by February 2017.
The other option for Switzerland is to use the safeguard clause and introduce immigration quotas to be decided annually by the federal government.
But this risks a sharp response from EU with risks to Swiss companies and an end to such things as EU research grants, European legal expert Christa Tobler, from the University of Basel, told NZZ am Sonntag,