Signing the 20-year-old was a high-profile coup for Celtic boss Brendan Rodgers this summer, but the French striker has not found the net in five friendlies and Champions League qualifiers so far for the Hoops.
Dembele arrived in Glasgow for a meagre £500,000 but the compensation fee does not reflect his potential, with the likes of Tottenham Hotspur and Arsenal both linked to the youngster prior to his Fulham departure last month.
Rodgers has made him wrestle with Griffiths for a spot up front, with the Scotland striker occasionally pulled out wide to facilitate Dembele through the middle so far.
The 26-year-old knows a thing or two about scoring for Celtic, having done so on 40 occasions last season under Ronny Deila, but things weren't already this good for Griffiths and the former Hibernian hitman has told his new team-mate to put the pressure to one side and focus on enjoying his football.
"I know from experience that it can take a while here," said Griffiths to the Glasgow Evening Times.
"You do feel under pressure when you need that goal. It'll be a massive relief for him when he gets it, I'm sure, but he just has to relax and allow his own game to come.
"Sometimes when you are under pressure you end up thinking too much about it. If you relax it just comes naturally."