Griffiths scored a hat-trick on his last trip to Rugby Park, while he was on loan at Hibernian last season.
The 23-year-old has struck four goals in as many starts since his January transfer from Wolves, including a treble last time out against Inverness Caley.
Griffiths told Celtic's official website: "It's always good to have the first game of the weekend out of the way and hopefully we can go there and put in another performance like we did against Inverness Caley Thistle and come away with the three points.
"I have scored a few goals against Kilmarnock, and I actually scored a hat-trick the last time I played there, so hopefully I can keep the run going with another goal or two.
"I don't like to set goal totals or anything like that and just want to take each game as it comes and if I can get chances I'm confident I can put them away."