Postecoglou will reportedly walk away from his position next month, even if Australia make it through to next year's World Cup by beating Honduras in an intercontinental playoff.
Cahill, who scored both goals in Tuesday night's 2-1 win in Sydney, didn't confirm whether he had spoken to Postecoglou since the report surfaced but said it's "only speculation".
A prickly Cahill insisted the focus should be on celebrating Australia's achievement in advancing to the final stage of World Cup qualification.
"It is just speculation," Cahill said on Thursday in Melbourne.
"I feel that this angle, the day after the biggest game in Australian soccer to qualify for a fourth consecutive World Cup, is not needed.
"I think we concentrate on celebrating a 2-1 victory, firstly, and looking forward to a full house at home in Sydney of 80,000-plus.
"Speculation is always going to come with our game and it is just disappointing it has come out the day after."
Cahill, who was promoting Melbourne City's A-League round two derby with Victory on Saturday night, insisted the players were not affected by Postecoglou's possible departure.
"It is called professionalism," he said.