Bielsa, 63, has Leeds sitting third on the English Championship table in his first season at the club, vying for direct promotion to the Premier League with his signature brand of attacking football.
The Argentinian coach has been linked with the head coach role at Roma by Italian newspapers La Gazzetta dello Sport and Il Messaggero along with four others.
It could be seen as an inflammatory appointment given his history with Roma's fierce local rivals Lazio.
Bielsa became Lazio coach in July 2016 but sensationally quit just two days later, prompting the angry biancocelesti to take legal action against him for breach of contract.
It's not the only unusual story about the coach nicknamed 'el loco' (the madman). He resigned from Marseille in 2015 just one match into his second season at the club, and was suspended then promptly sacked by Lille in 2017 after just 13 games in charge.
He also courted controversy this season when he admitted to spying on all of Leeds' opponents.
The other coaches linked with the Roma job, where Claudio Ranieri is currently caretaker, are Chelsea's Maurizio Sarri, Atalanta coach Gian Piero Gasperini, Sampdoria's Marco Giampaolo, and Leonardo Jardim of Monaco.
