The government will discuss if the amount of work permits issued to third country nationals should be cut.
Cantons and businesses are against the move.
Third countries are those not in the EU or EEA which fall under free movement agreements.
The Federal Council currently has a limit of no more than 12,000 permits a year to third countries – which now includes the UK.
But the Justice Minister, Elisabeth Baume-Schneider, wants to cut that to 9,600.
But the Employee Association is critical of the cut. It says there are specialized workers not found in Switzerland or the EU and are important.
A final decision on the quota number will be made in the next few weeks.
Parliament rejects WHO alcohol policy
Cyclist dies near the UN
Govt may buy fewer F-35s due to cost
Amnesty slams Bern police
Two men given house arrest after stealing vignettes
What's likely under the tree this year?
