The Sun says there has been increasing tension and things are believed to have come to a head at the Kop outfit's Melwood training ground on Thursday.
Ayesteran is said to be unhappy at being increasingly marginalised.
He also wanted to be consulted over the appointment of fitness coach Paco de Miguel, who was sacked by Valencia.
De Miguel is now set to replace Ayesteran as Benitez's No 2 at Anfield.
Ayesteran has quit the club on immediate leave while the details of resolving his contract are agreed.
Benitez said: "He said he'd like to leave and we're looking at the situation.
"We've had 11 years working together and it did surprise me a little bit."
Benitez had given full control over training and preparing the squad to Ayesteran - but this was altered in pre-season.