Lampard has been out of work since being sacked by Chelsea a year ago, though he was linked with jobs at Rangers and Norwich City in recent months.
Now it looks like the former England midfielder could be heading back to Premier League management with the vacancy at Goodison Park.
Everton had been looking to hire Vitor Pereira, but the move was met with such a backlash from fans that Lampard now looks to be in pole position for the job.
Lampard is set for further talks with Everton chiefs, who seem to have backed down on potentially hiring Pereira, who clearly wasn’t to the liking of the Merseyside giants’ supporters.
There may still be other candidates in the frame, with former World Cup-winning Italy centre-back Fabio Cannavaro also mentioned as an outsider for the role.
Lampard would be an intriguing appointment after doing some promising work at Chelsea, as well as at Derby County before that.