Finkler's tenure had been in doubt after Kalezic suspended him for disciplinary reasons following a petulant reaction to his 55th-minute substitution in Wellington's 4-1 loss to Central Coast two weeks ago.
His departure leaves the Phoenix with options in the January transfer window, although it appears unlikely Kalezic will be looking for a midfield replacement for the Brazilian.
"In that position, we have a couple of players — Dario Vidosic, Michael McGlinchey — so hopefully we can spend that spot for some other position we think the team needs more at this moment," Kalezic said.
"There are two positions, and we have to decide very soon which of those two we want to replace."
Kalezic didn't elaborate further, saying his focus was now on next Sunday's match in Perth, where Wellington will be boosted by the return of injured striker Roy Krishna.
"I haven't spoken with the club, I was concentrating this week on the game we played [on Saturday], and I think our focus has to be on the next game in Perth. When we fly back, we have all the time to sit with the board and make decisions."
- NZN