The 25-year-old has been sensational for the Scottish Premiership leaders this season.
Despite failing to score during the Hoops' victory over St Johnstone at the weekend, the former Wolves forward has been in scintillating form for Ronny Deila's side this season, scoring 20 times in just 20 league appearances.
That form has led to Chris Hughton monitoring the Scotland international (via Record) as he looks to bolster his attacking options in an attempt to keep their place in the promotion race.
While the Seagulls are currently third in the division, just five points adrift of league leaders Hull City, they have scored the fewest goals of any side in the top ten, so could certainly do with a ruthless finisher, such as Griffiths, if they wish to earn a place in the Premier League next year.
However, with Griffiths signing a new long-term contract that will keep him at Parkhead until 2019 (via Record), the Bhoys are clearly planning to keep the forward as a focal point of their side for several years to come.