The Toffees have been interviewing several names from their shortlist of managerial candidates in recently days as they look to find a replacement for Benitez.
Former Porto coach Vitor Pereira had emerged as the frontrunner to land the Goodison Park hot seat but a strong backlash from some sections of the Toffees faithful has seen his chances of job diminished.
Ex-Chelsea boss Lampard is another name in the frame to take over at Everton and he was interviewed last week by the club.
And the Merseyside giants are now set to interview the 43-year-old for a second time today as they step up efforts to find a new man to lead the club.
Lampard has been out of work for over a year since losing his job at Chelsea but could now return to Premier League management in the Everton dugout.
The former Derby County boss also held talks with Crystal Palace, Aston Villa and Norwich City since leaving Stamford Bridge but the Everton hierarchy are seriously considering him to take the reins of the club.
It remains to be seen whether Lampard can convince Everton that he is the right man to turn the fortunes at the club and help them climb away from the drop zone.
