Mayor Denis Coderre dismissed rumours Parent, who was appointed in 2010, is quitting because of a dispute between the chief and the city administration.
Coderre insisted he was ready to extend Parent's contract and that he had the go-ahead to do so from the province's public security minister.
Parent did "extraordinary" work given difficuilt circumstances, the mayor said.
Parent's reign was marked by two cases in which officers were accused separately of selling information to members of organized crime networks.
He also had to cope with the often-violent student protests in 2012 as well as a 2014 protest at city hall where police stood by while municipal workers vandalized parts of the building.