The Basques are hoping to convince the Argentine to accept a new deal and continue the good work he has already done at San Mames
The Argentine's current deal expires in the summer and he was heavily linked with Barcelona before the Catalans decided to appoint Tito Vilanova to succeed the outgoing Pep Guardiola as boss.
Amorrortu is desperate to tie Bielsa down to a new contract after a season in which the Basques have impressed many with their stirring run to the final of the Europa League.
"This is a coach who has improved all of the players, not just the team," the Athletic director is quoted as saying by AS.
"We need to find an agreement because it is fundamental for the consolidation of all that he is doing.
"And I have to say that the super-professional relationship with Bielsa is still being maintained and strengthened.
"He has taken on the role that we were all hoping he would, and he is giving us a lot of lessons that will serve us well for the future of Athletic."
Amorrortu also revealed that the club are in the process of trying to convince in-demand striker Fernando Llorente to remain at San Mames.
"We are working on many situations and obviously he is key for the future," he added.
Bielsa and Llorente are currently preparing for Wednesday's all-Spanish Europa League final against Atletico Madrid in Bucharest.