The Rosario native appeared downcast after his side's Europa League and Copa del Rey final defeats, but it has been rumoured that he has already decided to continue at San Mames
The 56-year-old coach is out of contract this summer and has to date been non-committal on his future with the Basque outfit.
However, Bielsa has applied for a new work permit that would allow him to remain in the country until 2014, according to EL Correo.
The former Argentina boss has drawn widespread praise for turning Athletic into one of the most attractive footballing sides in Europe but was hit hard by the club's 3-0 defeats to Atletico Madrid and Barcelona in the finals of the Europa League and Copa del Rey, respectively.
Bielsa took full responsibility for both losses and admitted after the Blaugrana beating that his future was still up in the air.
However, there has been mounting speculation that the Rosario native this week informed his players and club officials that he would be continuing at San Mames for another season.