Poor results and dwindling crowd sizes are also heaping pressure on their place in the A-League as they continually try to justify their licence.
Kalezic arrived with a solid CV after several coaching roles in Europe.
The 48-year-old replaced stand-in coaches Des Buckingham and Chris Greenacre, who took charge for the second half of 2016-17 following the departure of head coach Ernie Merrick.
Kalezic's assistant coach was proven A-League mentor Rado Vidosic but he departed just before Christmas, citing a difference in methods to the head coach.
It also prompted the exit of Vidosic's son and Australian international striker Dario, who was a key off-season signing.
Pressure has mounted on Kalezic in recent weeks as his team lost four of five games, dropping out of playoff contention while playing an unattractive style of football.
It is unclear if Kalezic will see out the six remaining games this season, with the club unavailable for initial comment.
It is still more than a week until they next play away to the Western Sydney Wanderers.
- NZN