Any transfer to this country would be contingent on negotiating an exit clause from his Japanese club as well as a release from the Mariners but the Herald on Sunday understands that is a probable, rather than possible, scenario.
McGlinchey was coy on the subject when speaking after the South Africa match.
"I don't really know where that talk has come from, to be honest," McGlinchey said. "Maybe a couple of the boys have started that. Maybe one day I guess but I am contracted to two clubs at the moment so I can't really be talking too much about it."
McGlinchey would be tailormade for the Phoenix. He wouldn't be a direct replacement for Carlos Hernandez - neither as creative nor as prolific in front of goal as the Costa Rican - but McGlinchey is arguably a much better fit. He is the box-to-box, attack-minded, creative midfielder the Phoenix have never really had.
Felipe was outstanding in his single season but was never a long-term prospect and Tim Brown had a remarkable workrate and eye for goal but didn't have the passing range and vision.
At 27, McGlinchey is coming into his prime. He's played more than 120 A-League matches, has upped his goal-scoring rate in the last two seasons and was one of the most influential midfielders in Australasia before leaving for Japan.
The schoolboy Celtic player has also become a mainstay of the national team and has now played 26 internationals (three goals) since his debut in 2009.
McGlinchey showed some nice touches on Friday night, linking well with Tyler Boyd and Ryan Thomas on several occasions as the All Whites constructed some neat passages in the final third.
McGlinchey admits his time in Japan hasn't gone to plan but accepts it's part of the game. "It's a great city and my family has enjoyed it but I haven't played as much as I would have liked and it does get you down a bit," McGlinchey said. "You want to be playing football.
"It has been disappointing. I had high hopes coming over to the J-League. It was where I wanted to be. It hasn't worked out, for whatever reasons. That's football. You just have to pick yourself up and hopefully get a crack and, if you don't, move on."
McGlinchey appeared in most matches under Arnold but game time has since dried up.
"The assistant manager has come in and gone back to what he knows best," McGlinchey said.
Meanwhile, McGlinchey is upbeat about the potential of the All Whites, as a youthful squad earned a meritious draw on Friday night.
"It's very exciting. The [young players] are fearless, in a way. You see them in training trying all their tricks and even out there. In the next four years we have a great chance to do something."
