The striker’s future remains uncertain with the Parkhead club having yet to decide whether to activate a year’s option tied to the end of a now concluded three-year deal he signed in September 2018.
But the 30-year-old, who has scored 123 times for Celtic since joining the club in January 2014, is hoping to be part of Postecoglou's plans after being left encouraged by an initial phone conversation with the incoming head coach this week.
"I spoke to the manager Tuesday morning and things seemed positive," Griffiths told Sky Sports "We'll have another chat at the beginning of next week when he's out of isolation and then we'll take it from there.
"It was a massive thing for him just to give me a phone. He didn't have to but he took time out of his day to give me a phone and gave me his ideas and plans mving forward.
"It was a positive chat. When he's out of isolation we'll have a chat face-to-face and see where we're at."
After being criticised by previous boss Neil Lennon over his fitness issues, Griffiths stressed he is working hard to return for the new season in top condition as he looks to address the question marks from last season, where he made only nine starts in all competitions after returning from lockdown overweight.
"I'm working every day. It was well documented I didn't come into pre-season after the last lockdown in the best of shape, and it’s been touted again this season. I’m working very hard and we’ll see what happens,” he said.
“People say I'm not fit enough to play games but I don't think I missed a training session for the last six months. I was always on the bench, I never missed a game and if Celtic ever called upon me I was fit and available to go.
“People that keep saying I wasn't fit enough to play games is crazy to me, but it is what it is. People are always going to have their own opinion.”
Griffiths, who scored a famous free-kick double against England in 2017, also addressed his international future and maintained that he is keen to win his Scotland place back after missing out on Steve Clarke’s 26-man squad for the Euros.
"I was disappointed but I don’t think I deserved a place in the squad,” he said.
“Other boys have been playing the full season and I’ve been playing a bit-part at Celtic. If I got in the squad I'd have been delighted but I think the boys that are in there just now, especially the strikers and forward players, deserve it.
"I want to be back here and help the team get to the World Cup in Qatar, but first of all I need to get myself in the best possible way I can to mae sure I'm in the plans for my club and country.
“It was well documented I didn't come in [last season] in the best of shape, so I'm in the gym every morning, doing pitch sessions as well, so we'll see what comes in the next couple of weeks.”