Sky Sports have reported that Everton have offered Benitez the managerial job.
Talks have been held between the Spaniard and the Toffees.
The 61-year-old is now claimed to be on the brink of returning to English football and taking charge of Everton.
Benitez has been without a managerial job since January 2021 when he left Chinese Super League club Dalian Professional.
The former Valencia boss was the manager of Liverpool from 2004 until 2010.
During his time at Anfield, Benitez won the FA Cup and the Champions League once each.
Liverpool and Everton are big Merseyside rivals.
Everton have been looking for a new manager since the start of this month when Carlo Ancelotti returned to his former club Real Madrid.