The 47-year-old was most recently coach of Saudi club Al Taawoun - for just seven matches - but most of his background is centred on continental Europe.
On the surface Kalezic doesn't have a particularly eye-catching CV, though he has a breadth of experience that would have appealed to the Phoenix.
Kalezic's coaching career began at Dutch club De Graafschap. After being assistant coach, he was promoted to the first team job near the end of the 2008-09 season. He couldn't prevent relegation, but managed the team's successful return to the Eredivisiethe following year by winning the Dutch second divsion.
He was then appointed manager of Belgian Pro League coach Zulte Waregem, but lasted only 21 matches (3 wins, 9 draws, 9 defeats) before being sacked with the club hovering above the relegation zone.
His next stop was Stockport County - then languishing in the fifth tier of English football - but departed after 12 matches "by mutual consent".
Kalezic then had two seasons in charge of PSV Enidhoven's Under-23 side, Jong PSV, in the Dutch second division, before being hired by Roda JC, notable in New Zealand as Ivan Vicelich's former club. He was dismissed by Roda after one season in charge, due to a falling out with their technical director at the end of the 2015-2016 season.
Kalezic had seven matches in charge at Al Taawoun, before stepping down in October last year.
According to Australian sources, his assistant could be Rado Vido.
The 55-year-old had a long coaching career at Brisbane Roar - mainly as an assistant - and has had similar roles at both Melbourne Victory and Sydney FC. If correct, his appointment would make sense, as it would provide a highly experienced A-League hand for Kalezic.
The Phoenix has refuse to confirm or deny reports linking Kalezic to the job, though all will be revealed on Tuesday morning.
Whoever the new coach is, it's vital they have the right man, as a significant turnaround is needed next season.
