The 22-year-old was handed the armband following the death of Phil O'Donnell in December but sat out the last five games of the season with a broken jaw following a nightclub incident.
This week Quinn was given 150 hours community service after being convicted of a nightclub assault which took place last August.
The Fir Park players reported back for pre-season training on Thursday where Quinn expected to hear his fate.
However, boss Mark McGhee has said that the issue had not been discussed.
"The players were in today for some fitness tests, nothing fancy", he said.
"I haven't spoken to Paul and I haven't decided anything yet. It will be the start of the season before I do."