Griffiths moved to Parkhead from Wolves in 2014, and his ambition is to play over a decade at the club, reaching the legendary status of current captain, Scott Brown.
"My representatives are working behind the scenes to try and get me a new deal," said Griffiths.
"The talks are in the early stages just now but, hopefully, we can get it done sooner rather than later.
"Hopefully, if we can come to an agreement, I'll not be far off [the time] Broony has been here. He deserves his testimonial.
"I've got another three years left on my contract as it is, but why would you want to go anywhere else? I'm playing at a top club with a top manager, in front of up to 60,000 in every home game.
"There's no reason to go anywhere else. We've got Champions League football every season. It's harder for us to get to the group stage now but when we do, those are memorable nights."