The Championship side are chasing promotion to the English Premier League but have hit a series of obstacles in their quest to bring in attacking reinforcements.
Football Insider, quoting a Leeds source, claims Scotland international Griffiths has been added to the club's shortlist as the transfer window enters its final ten days.
Griffiths, 29, started and scored against Partick Thistle in the Scottish Cup fourth round at the weekend but a regular starting berth looks somewhat unlikely with Odsonne Edouard and new signing Patryk Klimala likely to be ahead of him in the pecking order at Celtic Park.
His contract at Celtic runs until the summer of 2022 but despite 108 goals and more than 40 assists in 222 games for the Hoops, his future at the club may be uncertain.
Leeds are tracking a number of strikers including Middlesbrough frontman Britt Assombalonga and Watford's Andre Gray.