It is believed that the players were informed of the news on Thursday after training, and it is not expected that Ayesteran will be alongside Benitez in the dug-out for Saturday's home game with Derby.
Liverpool would not confirm any further details, although Benitez said: "Paco has told me he wants to leave, apart from that I cannot say any more. We will have to assess the situation."
It is not known whether Ayesteran has been offered another job in Spain or whether he wants to return home for personal reasons.
But the disruption to Benitez's backroom staff will be massive. Ayesteran has been in charge of fitness coaching, but also handles much of the squad administration.