The Cherries announced today the Spaniard will be moving on when his contract expires at the end of the current campaign, creating a Premier League vacancy.
Former Celtic boss Postecoglou remains out of work after his October 2025 sacking following just three months in charge of Nottingham Forest.
He has previously stated his wish to start his next job in the summer so he has a pre-season to work with his new players, so Iraola's departure would provide that opportunity.
And bookmakers have made the Australian 6/1 second favourite for the job, behind Ipswich Town boss Kieran McKenna, who is priced at 4/1.
The other names in the mix are Mauricio Pochettino (6/1), Marco Rose (6/1), Eddie Howe (8/1), Edin Terzic (8/1) and Thomas Frank (8/1).
Postecoglou has been working for a Technical Observer for UEFA but made no secret of his wish to get back into management.
He said: “I’ve figured out that for me to do what I do, the start of pre-season is a good starting point,
“Jumping in mid-season – especially in the Premier League but in most leagues – is just probably too much of a challenge for the way I do things. That’s what I’m holding out for.
“Where that is and what it looks like is hard to say at the moment, but I haven’t even scratched the surface of what I want to do over here yet and the impact I want to make, the football I want to play.”