Derek McInnes' Dons have finished as runners-up in each of the past two seasons with the gap between the sides sitting at 12 points with two matches of the season remaining.
Celtic officially clinched the league title with a 3-2 win at home to Aberdeen on Sunday. Despite the arrival of new club The Rangers in the top flight for the first time and Hearts looking to build on their third place finish, the Scotland striker expects the Dons to remain the greatest threat to six-in-a-row.
Asked who he believed would provide the best challenge to his side, Griffiths said: "Aberdeen again I would say.
"I'm sure Derek [McInnes] 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."
Source: STV