The Sun says former England international Lennon is injured and last played in mid-December.
And the blow to his knee means he may not be able to play again this campaign.
But Marcelo Bielsa is compiling his background checks on the speedster as he plots a swoop to being the hometown hero back to Leeds.
Lennon joined the Turf Moor outfit a year ago after battling mental health issues with previous employers Everton.
He has cemented himself as a vital member of the Burnley squad since, playing 22 times so far this season, and helped them qualify for Europe last May.