The Parkhead club are still to appoint a new boss with Eddie Howe talks having broken down.
Yokohama F. Marinos manager Ange Postecoglou is the favourite to take on the post.
Logan, however, had his own fun with the current turbulence at Parkhead, posting an image of him holding a Celtic scarf above his head on Twitter.
He noted he didn't really want to be Celtic manager but no one else wanted it.
“Thought I'd make my first role in management a small one and build it up from there," he posted.
"I can't say I'm happy for the role but hey a jobs a job no one else wanted it.”
The 33-year-old has had a tempestuous relationship with Celtic supporters during his time at Aberdeen.
He was involved in an incident with former Parkhead winger Aleksandar Tonev in 2014. The Bulgarian was found guilty of racially abusing the former Manchester City youngster.
Logan, who enjoyed a positive spell at Hearts in the second half of the season, spoke recently about his battles with Scott Brown and that the incident is in the past and he has moved on.
“We've had a little bit of argy bargy on the pitch, and for me that's where it stays,” he said.
"Anything else to do with other stuff, where people might be saying about him backing Tonev with all the racism stuff, I've left all of that in the past.
"It's so far gone that I only ever think about it if someone brings it up."