The club's board of directors met at 11:00 to discuss Cotter's position following criticisms he made against both the club and some players during an interview with La Montagne newspaper.
A group of about 100 fans had gathered in front of the club's Marcel Michelin stadium, where the board was meeting, from about 10am local time to show their support for the coach.
Following Cotter's La Montagne interview last Wednesday, Clermont president Rene Fontes said he was "stunned" and "disappointed" and claimed Cotter had offered his resignation.
That was something the 51-year-old coach denied last Thursday, claiming he intended to see out the remaining year on his contract.
Having joined the club in 2006 after a successful period as part of the Canterbury Crusaders coaching staff, Cotter led Clermont to the 2010 Top 14 title.
However, he has so far been unable to add to that trophy, or land a first ever European Cup triumph.
This year they reached the final but lost out 16-15 to Toulon while they also crashed out to Top 14 winners Castres in the domestic semi-finals, despite being widely acknowledged as the best team both in France and Europe this season.
Last season they bowed out in the semi-finals of both competitions and have picked up a chokers tag under Cotter, who is due to take over as Scotland coach when his Clermont deal comes to an end.