The framework agreement is designed to put to bed certain key institutional questions regarding Switzerland's bilateral arrangements with the EU.
The talks are vital to Bern in ensuring continued access to the European Common Market.
But the negotiations, considered to be a possible indicator of how post-Brexit relations between the UK and Brussels play out, have stalled.
However, on Wednesday Swiss foreign minister Ignazio Cassis is set to unveil a deal aimed at breaking the deadlock, Switzerland's SonntagsZeitung reported.
Under the terms of the deal proposed by Cassis, Brussels would accept a more limited role for the European Court of Justice (ECJ) in Swiss affairs in exchange for Swiss concessions on its special controls on EU workers in Switzerland.
Specifically, EU legal issues would be dealt with by the ECJ. But in the case of disputes between Brussels and Switzerland over new EU laws and their impact on bilateral agreements, these would be dealt with by an arbitration panel.
In exchange, Switzerland would consider tweaks to its eight-day rule, which requires foreign companies to inform Swiss authorities at least eight days before they carry out work in Switzerland so that the Swiss can ensure firms are not bringing in cheaper labour to undercut high wages in the Alpine country.
Under the Cassis deal, Switzerland could shorten this eight-day period but Bern would still be entitled to carry out a range of checks on foreign workers. This would be the case even though these measures contravene the principle of free movement in the EU.
The foreign minister is now looking for the Swiss government to back his proposed deal with Brussels.
But unions say the negotiation process is being carried out in bad faith. In a policy paper, they argue their advice from officials in Brussels is that the EU will not accept measures including on-the-spot checks of EU workers on building sites.
These are viewed as harassment by the EU, unions say, arguing that Brussels is far more interested in a homogeneous economic area than the rights of workers.