The 28-year-old joined the Scottish champions from Wolverhampton Wanderers on a four-year deal in January 2014 and two years later penned a new deal keeping him in Glasgow until 2021.
The Scotland international, who scored 13 goals in all competitions for Brendan Rodgers's side last term, has been in discussions over a fresh extension for some time and has revealed that an announcement is due imminently.
"It's still ongoing, these things are never easy, but it's almost completed now and hopefully in the next couple of weeks it will be done and dusted," he told Sky Sports News.
"It's been going on for a number of months now and these things aren't easy to deal with, so hopefully in a couple of weeks it will be done.
"I'm not very sure about the length of the contract. That's something my representatives in the club will deal with and hopefully it's a nice, long contract."
During his time at Celtic, Griffiths has a record of 73 goals in 123 Scottish Premiership appearances.