The 30-year-old faces an uncertain short-term future.
Griffiths’ contract with the club expires this summer but they hold a one-year extension option.
It is understood no decision will be made until the new manager is in place.
The striker, who has scored more than 120 goals for Celtic, is aware he could have to look for a new club.
Hibs and Aberdeen have both been linked with the player.
“The focus for me over the summer is to get as fit as I can and be ready for pre-season wherever that is and hit the ground running,” Griffiths told Go Radio.
“I need to wait on the new manager getting announced and see what plans he has for me. If he doesn’t see me in his plans then it’s off to pastures new.
“If that’s the case I’ve had great years at Celtic and put myself into the history books in the top 20 goalscorers.”
Hibs boss Jack Ross has spoken previously of his admiration for the player and didn't rule out a possible move for him if he became available.
He said: “It is an easy connection to make because of his association with the club and his time at Hibs before but I would temper that by saying, is he a player we have admiration for? Of course, because his goalscoring record is up there with the best in Scotland over recent years.
“It may be something that should the opportunity arise, it would be something we’d discuss.
“But it’s not something we have been able to discuss in any detail because he’s not a player, as of yet, who will be available.”
Meanwhile, Griffiths also admitted his place in the Scotland squad for the Euros wouldn't have been merited after the season he has had, starting just nine times.
He said: “I’ve not played enough football this season so I don’t think my place would have been merited. Guys like Kevin Nisbet and Lyndon Dykes have been scoring goals and deserve it.”