Cahill and FFA have long been at an impasse over the governing body's attempts to bring the Socceroos' most commercially valuable name to the domestic competition.
A war of words escalated in February after Cahill's shock axing by Chinese Super League club Shanghai Shenhua.
FFA chief executive Gallop stated he and other parties had tried to sign Australia's leading goalscorer only to be told the A-League could not "meet his needs", a claim Cahill firmly denied on social media.
It came after Cahill heavily criticised the A-League's lack of vision he felt would hurt his career.
With his six-month contract at Hangzhou Greentown about to finish, the veteran striker is again pondering his future.
But while reports suggest Cahill is poised to re-sign with Hangzhou or shift to another club in China, the 36-year-old regurgitated a familiar refrain on Tuesday in Sydney.
"I've never closed the door on the A-League," he said in Sydney on Tuesday ahead of the Socceroos' two-match friendly series with Greece.
"It's obvious that there never has been any contact with me... I never had a phone call.
"I'm very close with a lot of people in the league, but I can't press the button on anything.
"I think it's going to be left down to the big boss man of the league to decide what he wants to do."
Cahill revealed on Tuesday he was carrying a "slight" hamstring issue but hoped he'd be fit for selection in coach Ange Postecoglou's line-up against Greece on Saturday night at ANZ Stadium.