Leeds sacked the Argentine in the latter stages of last season in order to bring in American boss Jesse Marsch.
Bielsa has regularly been linked with a return to the Premier League amid suggestions he is keen for another crack at the English top flight.
He was mooted as a contender for the Bournemouth job, but the Cherries went in another direction; Bielsa could now end up on Merseyside.
It has been claimed that Everton are now in touch with Bielsa, with talks having been opened.
Bielsa is suggested to be one of the main candidates that Everton are looking towards as they try to replace Frank Lampard.
If he takes charge at Goodison Park, Bielsa would come face to face with former club Leeds in the middle of February.
Leeds are also not clear of the relegation scrap, with second bottom Everton having only collected three points fewer than the Whites.
