Swansea face West Ham at the weekend.
The two sides face off on Sunday afternoon, and Bielsa is reported to be Swansea's preferred option to replace Garry Monk, who was sacked last week.
The fact the opponent is West Ham is of particular interest, after he was linked with the Hammers job in the summer.
Former defender Guy Demel, who was released from West Ham in the summer, told The Mirror in June after Slaven Bilic was appointed, that Bielsa was the manager the club's players were particularly interested in.
He said: "When the rumour came out we talked about it in the locker room with Morgan Amalfitano and other French-speaking players.
"Given the results and the performances of Marseille, we thought Bielsa would be a good choice but unfortunately for West Ham, it didn't happen."
Bielsa is out of work having walked away from Marseille in the summer, and is renowned for his unconventional approach.
He is a fascinating manager, who implemented a 3-3-1-3 formation for both Argentina and Chile at international level, and enjoyed success with Athletic Bilbao in Spainb.
For West Ham their appointment of Slaven Bilic appears to have worked out well anyway, currently eighth in the Premier League, but if they do come up against Bielsa this weekend it will be an interesting look at what they could have had instead.