The Toffees are in the middle of a search to bring in a new manager after they sacked Rafael Benitez earlier this month.
Interim manager Duncan Ferguson failed to inspire Everton last weekend as they slumped to another defeat at home to Aston Villa.
Vitor Pereira has emerged as the favourites to become the next Everton boss and is scheduled to hold more discussions with the club over the next few days; it was claimed in Portugal he is set to take the job.
Lampard has been in the fray as well and it has been suggested that the former Chelsea boss will discuss the role with Everton this week.
It has been a year since he was sacked at Chelsea and he is keen to return to managing in the Premier League.
He is on Everton’s radar and talks have been scheduled to take place between the club and Lampard this week.
Wayne Rooney has also been linked with the job but so far, Everton are yet to establish contact with him.
There is no imminent arrival of a new manager at Everton but a decision could be made this week.
