Bielsa has been out of work since he left Leeds at the end of February, having been sacked by the Whites, and is looking to return to football management.
The Argentinian had a fruitful spell at Athletic Bilbao previously where he took them to the final of the Europa League in his first season.
It emerged on Wednesday that Bielsa has all but agreed a return to the club with one of the presidential candidates.
And according to the local Bilbao radio station Radio Popular, Arechabaleta is the one who has worked out an agreement with the 66-year-old.
He has already announced that he will bring in Ramon Planes as a sporting director if he becomes the next Athletic Bilbao president.
And he now has an agreement in place with Bielsa to get him back to the club as head coach if he comes out as the winner in the elections on 24th June.
It has been claimed that Arechabaleta has not ruled out announcing Bielsa’s name next week to further boost his chances of winning the election.
The Argentinian has remained a cult figure at Athletic Bilbao despite leaving the club almost a decade ago.