The Toffees have been in advanced talks with the former Wolverhampton Wanderers head coach over the last few weeks, but no agreement has yet been reached.
Even though the potential arrival of Benitez could cause widespread backlash amongst Everton supporters, according to talkSPORT, the club's owner Farhad Moshiri is open to the idea of brining the Spaniard to the blue side of Merseyside.
Everton were not expecting to be in the hunt for a new manager this summer, however Carlo Ancelotti decided to leave the club after 18 months in charge and return to Spanish giants Real Madrid, replacing Zinedine Zidane at the helm.
After leading Liverpool to Champions League glory in 2005 and winning the FA Cup a year later, Benitez is admired by the Reds as one of the club's greatest ever managers.
The 61-year-old has also had spells with Premier League duo Chelsea and Newcastle United as well as Inter Milan, Napoli, Real Madrid and Valencia.
Benitez's most recent managerial role was with Chinese outfit Dalian Professional, but in January he decided to leave after 18 months in charge, citing the health and well-being of his family during the coronavirus pandemic as one of the reasons for his departure.