Griffiths believes Hearts and Rangers will both be strong.
The Bhoys are targeting a sixth straight Scottish Premiership title in 2017, having been crowned champions ahead of the Dons at the weekend.
Rangers' promotion has whet the appetite of many neutrals ahead of the new campaign, with the Light Blues looking to challenge their Old Firm rivals immediately.
But Griffiths, the recently-crowned PFA Player of the Year, says Derek McInnes' men are the ones to beat.
When asked which club would run Celtic the closest next term, the 25-year-old told STV: "Aberdeen again I would say.
"I'm sure Derek and their management team will go away and strengthen and push us again but hopefully with the new manager coming in [at Celtic] we will strengthen as well. We'll look to go and make it six."
He added: "They [Aberdeen] pushed us all the way this season like they did last season. Rangers will come up and make a strong bid and Hearts will strengthen as well."
Despite being Celtic's closest challengers this season, Aberdeen, whose hopes were ended by the Bhoys on Sunday, are 12 points worse off heading into the final two fixtures.
But even with a margin as great as that a busy summer awaits for the champions, whose Ronny Deila is being replaced, leaving behind a squad comprising more than 30 senior players.
Rangers, meanwhile, have been linked with a string of ambitious transfer targets as they look to make the leap from Championship to Premiership contenders, notably Jordan Rossiter, Grant Hanley and Danny Graham.