The Scottish international forward is being targeted by the SPL giants, according to a report in Scotland today.
But he has not lived up to the lofty expectations that were held of him at Craven Cottage. He had scored 29 goals for Leeds in the 2013-14 season, but has managed just 14 this term in a campaign which has seen Fulham at the wrong end of the Championship table.
The report claims that Celtic are looking for a new striker as Manchester City loanee John Guidetti is set to find a club elsewhere next season, after an up-and-down season on loan in Glasgow.
They also claim Celtic watched the ex-Leeds captain in action against Charlton Athletic at The Valley on Tuesday, a game in which he scored the opening goal.
The striker is a former Rangers youngster but made a name for himself at Motherwell before embarking on his Football League career.
At 28-years-old the Scotland international may crave a potential run in the Champions League and a return to his home-town, although Celtic will need to compensate Fulham fairly handsomely for the privilege.