The Phoenix's season ended with a 4-0 dead-rubber loss to Macarthur FC, ensuring they finished just shy of an A-League Men finals spot after eight weeks under Greenacre.
Greenacre had taken the helm after Giancarlo Italiano resigned in February, falling on his sword after a 5-0 derby defeat to Auckland.
The Phoenix were 10th and winless in their last five games in their third season under Italiano, after an 11th-placed finish last season.
Italiano had taken the 'Nix to a second-place finish in his debut 2023-24 season.
Wellington finish this year's campaign in eighth after just nine wins.
Englishman Greenacre is in his fourth stint as Phoenix interim after playing 84 games from 2009 to 2012 for the club as a striker.
He was leading the club's academy development program before being given the call-up to replace Italiano.
Also the New Zealand under-20s coach, Greenacre was adamant he wanted the full-time gig.
"Of course, this club is in my blood and I've been here a long time and given a lot to it," Greenacre said.
"I've had some healthy discussions with the club in the recent weeks and we'll probably sit down next week and see how things go.
"They've supported me. I think the relationship's been pretty good from both sides."
Greenacre described their performance against the Bulls as a "blip", with a dejected 'Nix firing just 12 shots to the home side's 26.
Macarthur scored three first-half goals in 34 minutes, with veteran Matthew Jurman drawing first blood in the sixth minute when his shot deflected off New Zealand international Bill Tuiloma.
"Really disappointed with the way we conducted ourselves in the first half - we were nowhere near the pace," Greenacre said.
"When I think the own goal went in, you just saw the body language of our guys was just kind of depleted us really, which is disappointing.
"It's the first time I've probably questioned our group.
"They've been awesome for a number of weeks now and that was probably our blip.
"Unfortunately, we don't have the opportunity to kind of fix that going forward now, so we're going to have to wait until next season."