The decision comes just hours after the Basque club issued a statement in which they publicly criticised the Argentine for an altercation with a construction company employee.
At a press conference on Thursday, Bielsa had admitted his frustration that construction at the club's Lezama training facility was not completed in time for the start of pre-season and accused the company responsible for not respecting the contract that had been signed.
However, Athletic distanced themselves from his comments on Friday and apologised for the coach's behaviour, while insisting that the contract with the construction company had been fulfilled satisfactorily up to that point.
The Basque side then called an emergency meeting at Ibaigane, which was attended by both club president Josu Urrutia and Bielsa.
|BASQUEING IN GLORY
|150/1||Athletic Bilbao are 150/1 with Bet365 to win La Liga next season|
However, nobody present spoke to the press afterwards and there has been no official word thus far on whether the 56-year-old trainer's resignation has been accepted.
Bielsa took charge of Athletic last summer, enjoying an impressive debut season at San Mames as he led the club to the Copa del Rey and Europa League finals.
He signed a new contract - valid until 2013 - in June to put an end to speculation over his future after being linked with Chelsea, Inter and Barcelona, among other clubs.