The Aussie Parkhead gaffer has been linked with a move away from the Hoops in recent weeks after a flurry of activity in the English Premiership saw the Chelsea and Brighton jobs become available in quick succession.
Postecoglou has impressed at Parkhead since his arrival last summer[/caption]
But the speculation hasn’t stopped there – as pressure mounts on ex Celtic boss Brendan Rodgers at Leicester City.
The Foxes sit bottom of the league having not won a game this season and some have tipped Postecoglou to be the man to replace Rodgers should he be given the bullet.
And Cahill insists that his former international boss has aspirations to manage at the top level but only once he completes the project he is undertaking at Parkhead.
Read More Celtic Stories
The former Everton and Millwall attacker even made a sensational comparison between Postecoglou and Steven Gerrard, who the Aussie chief could follow in the footsteps of should he make the move south.
He told the Sydney Morning Herald: “If there’s interest now, that means there’s interest later.
“He’s someone that will probably have aspirations of coaching in one of the biggest leagues in the world.
“But at the same time, he likes to see out projects.
Most read in Football
“There’s always going to be question marks asked about jumping to the next level, and it’s just about whether he feels ready to leave one of the biggest clubs in Scotland.
“You see, with Steven Gerrard at Rangers, it’s sort of like a copy and paste – except Ange is on a different level when it comes to the way that he plays.
“That next step will be about making the right decision.
Read More on The Sun
“You look for longevity, and in football, there’s no guarantee, and to reset up and go again.
“It’s going to be difficult, but a challenge that every coach, I suppose, looks to.”