The forward has had a season marred by fitness issues for the club and the country. He only scored seven goals last season and was excluded from Steve Clarke’s Euro 2020 squad.
Celtic are yet to decide whether or not to activate an option to extend Griffiths’ contract for another year, leaving his career in limbo this summer.
Preseason training kicks off next week and it remains to be seen if Griffiths will be involved when the squad reunites.
However, the 30-year-old appears to be working hard to try and prove himself to new Celtic Park boss Postecoglou and his potential suitors.
He shared a story on his Instagram Story in the Gym with the message ‘we keep working’ just hours after the former Australia boss was confirmed for the role.
With people like Odsonne Edouard looking to leave the club this summer, Celtic could be running out of a proven striker with Albian Ajeti struggling for form last season.
Vakoun Bayo is the only other first-team striker to sign for the next term as he returns from a successful loan spell at Toulouse.