The 21-year-old was linked with a move to Glasgow over the summer, but the Hoops instead opted to bring in Shane Duffy on loan from Brighton.
The Republic of Ireland captain has struggled to produce his best form in Scotland, however, and Sky Sports – who conducted an interview with McKenzie over a potential move to Parkhead – have suggested that Neil Lennon could still be in the market for defensive reinforcements in the coming weeks.
American talent McKenzie, who has been capped at senior level for the US national side, is still understood to be on their list of targets, and the player himself has made it clear that he is not averse to a switch.
When asked whether he would still be interested in signing for the Bhoys, he said: "Yeah, ultimately it's about the situation being right for all parties.
"As the player you are probably the most important piece in the puzzle, but it's about making sure it's right for the club I'm at now but also the club I could potentially be going to.
"I want to be playing regular and consistent minutes - at least fighting for my spot and then trying to keep that spot. That's the most important thing. It's something I've obviously talked to my agents about and talked to the club and staff about and make sure it's right for everyone.
"I've done my fair share of research [on Celtic and the Scottish Premiership] and I've always loved football so I've known about Celtic for a while. You hear about Celtic and the path of Virgil Van Dijk - going from there to the Prem.
"I'm no dummy when it comes to understanding the leagues. I have a general idea of what the leagues look like and keeping up with who is at the front of the pack in the league race and tournaments. I know about Celtic and the league - and a lot of other leagues. But it's an exciting time, though."