The Scottish Sun report that United want the prolific striker to front their attack next season as they look to climb out of the football league for the first time since being relegated from the Premier League in 2004.
Leeds have been one of the English Championship’s lowest scorers this term with only 50 goals scored in 46 games.
Owner Massimo Cellino is said to be very keen on the Scottish international who he sees as the player to reverse the club’s fortunes in front of goal.
However, it may take more than £1m to persuade Celtic to part with a player they reportedly paid the same amount to sign from Wolves in last year’s January transfer window.
After a slow start to his career at Parkhead, Griffiths has had a great 2015 with 15 goals in his last 20 games, including a pair of hat-tricks.
He is contracted until 2018 on a reported £8k a week wage.
Meanwhile, Rotherham United are the latest side to be linked with midfielder Rodolph Austin, who was last week released by the Whites.