The Australian was strongly linked with the Brighton & Hove Albion job before Roberto De Zerbi was appointed, while if Brendan Rodgers was to depart Leicester City Postecoglou would likely see his name touted as a potential candidate to replace the Northern Irishman.
Such links are expected due to the excellent work he has done with Celtic since taking over last summer.
Speaking to Fox Sports Australia, Postecoglou played down any exit talk with an easy-going approach to his future, using what he tells his players as an example.
"It's not really on my radar," he said.
"It's a bit like our players, I keep saying to them that if they do what they do well, all this other stuff takes care of itself, whatever their ambitions or my ambitions may be.
"My ambition's always been the same wherever I've been, to be as successful as I can.
"I've charted a course that's got me to where I am today, I've just tried to do it to the best of my ability and opportunities arise from there.
"Right now, I'm at a massive football club. I'm living the dream, I'm enjoying every minute of it, and I'm determined to bring as much success as I can to it while I'm here."
Postecoglou saw Celtic beaten in the league for the first time in nearly a year on Sunday when they went down 2-0 to St Mirren. They still lead the Premiership by two points and have one point from two Champions League games.