The council discussed the city manager's performance during closed session Monday and decided to hold a special meeting next week on the issue.
The time of the meeting has yet to be determined.
"They've been unable to deal with the city manager position due to the limitations of the Municipal Code," said City Attorney William Curley.
The council placed Quincey on paid leave of absence on Jan. 4. An Upland code provision prohibits the council from removing the city manager within 180 days of an election if a new council member is elected.
Councilman Gino L. Filippi was elected on Nov. 2.
The 180 days end this weekend.
Filippi said he does not know what decision will be made during the session.
"I think it's time that we make a decision," Filippi said. "Obviously the residents are concerned about the unrest, and something needs to happen so we can move forward."