The national team coach guided Australia to the tournament finals in Russia with a 3-1 win over Honduras on Wednesday night.
On Thursday, he revealed a two-week timeline to confirm what comes next.
"I'm determined to enjoy this and determined for everyone to enjoy it," Postecoglou said at a public event in Sydney's Martin Place on Thursday.
"I understand the conjecture ... it's not about me trying to keep people in suspense.
"I'll have those discussions with David and Steven in the next two weeks and it will all be resolved."
A bombshell report last month suggested Postecoglou would walk from the job even if he was successful in his quest to become the first Australian coach to successful qualify for the World Cup.
That scenario has now arrived for the Socceroos and both the coach and FFA are keen to resolve the situation.
With no international fixtures until March, the next engagement for the Socceroos is on December 1 - the World Cup draw.
Gallop, speaking at the same event on Thursday, said a public confirmation would come before Australia's group stage opponents are confirmed.
"It's hard to imagine going to Russia without him. On that basis it'll be good to get clarity quickly," he said.
"The arrangement has always been to get through last night and talk about it. That's what we'll do."
Postecoglou has failed to clarify his position over the past month, lashing out at critics and those seen as not offering full support to his team.
After Wednesday's win, he turned in a typically enigmatic performance during his media engagements, saying he felt like an "outsider".
"I've been coaching for 20 years. I won my first championship when I was 31 years old. And you know what? I could coach for another 20 years and I'll always be an outsider in Australian football," he said.
"That's fine. I wear that as a badge of honour.
"I've had a hell of a lot of support from players, coaches and the general sporting public.
"That's all I need. The people that don't get me, they'll never get me."
The crunch coaching talks sit alongside the FFA AGM at month's end as significant moments for the sport.
Gallop was one of many breathing a sigh of relief that the Socceroos made it to Russia.
"In campaigns of the past, qualification was regarded as almost a make or break for the sport," he said.
"Now, it's not necessarily that.
"If you look across the next week, we've got A-League matches ... W-League, the FFA Cup final, Matildas games against China.
"There's a length and breadth to this sport that's unique to the country."
