Appointed less than a year ago to replace Spaniard Rafael Benitez, the 44-year-old former star player of Chelsea failed to get the other club in the city of Liverpool, current 19th in the Premier, off the ground. League, level on points with bottom side Southampton.
Last season, the club had narrowly ensured its maintenance by finishing in 16th place.
On Saturday, Everton lost 2-0 at West Ham, another club struggling to avoid relegation.
This ninth defeat of the Toffees in the last twelve Premier League matches was one too many.
Asked by Sky Sports after the meeting about Lampard's future, club owner Farhad Moshiri said: "I can't comment. It's not my decision."
"These things are not my responsibility. It's my job to work, to concentrate and to keep my head down," said Lampard.
A former iconic Chelsea player from 2001 to 2014, author of numerous goals for a midfielder (177 goals in 609 Premier League matches), Lampard notably won three league titles, four FA Cups, a Champions League ( 2012) and a Europa League (2013) with the Blues.
He has 106 caps (29 goals) for England.
Converted to coach in 2018, he led Derby County (second division) for a season before returning to his former club Chelsea, as successor to Italian Maurizo Sarri, who left to coach Juventus.
After a successful first season (4th) and qualification for the Champions League, the next one is more complicated.
In January 2021, he was sacked when the club was ninth in the standings.
He then bounces back to Everton where he succeeds Rafael Benitez.
But after the maintenance obtained at the end of the first season, the Toffees are currently stagnating in the depths of the classification, arousing the anger of the supporters.
Of the 44 matches led since his arrival at Everton, Lampard has a record of only 12 wins for 8 draws and 24 defeats.
© 2023 AFP