Lampard sacked by Everton after less than a year in charge
Lampard arrived on Merseyside at the back end of January last season, helping the club to narrowly avoid relegation from the Premier League in the 2022-23 season.
However, a poor run of form in the league - including a recent 2-0 loss to fellow strugglers West Ham on Saturday - has cost the former England and Chelsea hero his job.
They also previously lost 2-1 at home to Southampton in a key relegation clash.
The Toffees are without a win in the league since a 3-2 home victory against Crystal Palace back in October.
Everton are 19th in the table, with only Southampton below them on goal difference.
Speaking about his own future after Saturday's defeat, Lampard said: "Those things are not my choice. It is my job to work, focus and keep my head down.
"I know there's things going on at the club but it's never been a consequence for me whether a chairman or board member is at the game."
Lampard leaves Everton with just 15 points from 20 games and only three wins this term - the worst win ratio in the division.
Supporters have been holding regular protests after matches - mostly targeted at the club's owners rather than the manager - with fans bemoaning the failure to find a return on their transfer investments.
They have also been vocal against the club's inability to replace stars that have been sold, notably Tottenham's Richarlison who left the club in the summer in a £50 million deal.
Former Burnley manager Sean Dyche, Argentinian Marcelo Bielsa and ex-Wolves and Spurs boss Nuno Espirito Santo are among the bookies' favourites to take the helm.
West Ham boss and former manager David Moyes is also being touted, as well as former player Wayne Rooney, who currently manages MLS side DC United and was linked with the job prior to Lampard's arrival.