Athletic Bilbao coach Marcelo Biesla has emerged as the favourite to take over at Barcelona amid reports that Pep Guardiola is ready to quit the Spanish champions.
Guardiola is thought to want an exit from the Nou Camp and take a break from football altogether.
Bielsa, who has previously been praised for his management style by Guardiola, has guided his side to the Europa League semi-finals this season.
Roma coach Luis Enrique, Arsenal boss Arsene Wenger and Barcelona legend Johan Cruyff have also been linked with the potential vacancy.