His fellow Spaniard and long-term friend had been Benitez's number two at Tenerife and Valencia before he followed the Reds chief to Merseyside.
It is believed that the players were informed of the news yesterday after training, and it is not expected that Ayesteran will be alongside Benitez in the dug-out for tomorrow'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.
utusanlfc : and I thought such backroom feud only occurs at the other club. But it seems clearly now that LFC is just one of them... One of my reason to love LFC is the way it has been handled... conservatively and no other big news aside from its football and players. We don't want a flamboyant manager like Morinhore or a pensioner like Alex or a big mouth like Wenger. What we have in Rafa is good... he talks on a correct issue, correct tone and even cynism. But with this new negative development... errr... hmmm.... lets hope nothing's change for the worse. We have been accustomed to seen Ayesteran sitting next to Rafa, holding his folder... which content tactical manouverings... why laa this silly thing happened?.... issshhh....