Duncan Ferguson has been named caretaker manager while the club pursue alternatives to Martinez.

Lampard, 43, is out of work after being sacked by Chelsea in January 2021.

Former Everton and Manchester United forward Rooney is in charge at Championship strugglers Derby.

Everton confirmed on Tuesday that assistant manager Ferguson would step up for now, having previously taken the caretaker role in December 2019.

Following the dismissal of Marco Silva, the Scot guided the team to five points from three games against Manchester United, Arsenal and Chelsea.

The 50-year-old Everton playing legend led training on Tuesday morning as the side prepares for Saturday's game against Aston Villa.

Belgium coach Martinez is admired by Everton's hierarchy despite being the first of five managers sacked by owner Farhad Moshiri in May 2016 after three seasons. But, despite exploratory talks, the Belgian FA insisted the 48-year-old would not be allowed to leave.

It remains to be seen if Everton return to Martinez, who would be yet another controversial choice by Moshiri, given his first spell ended in fan fury and public protests demanding his removal, but other options are being looked into.

Rooney, 36, has been in the Everton board's thoughts since former Liverpool manager Benitez was sacked after seven chaotic months following Saturday's 3-1 defeat at Norwich City.

With Martinez currently off limits, the club must now decide whether to firm up their interest in Rams boss Rooney, who has impressed against a backdrop of financial meltdown and points deductions at second-bottom Derby.

Or to move for Lampard, a former Rams manager who had an impressive first season at Chelsea when he took them into the Champions League and the FA Cup Final, before being dismissed a year ago.

Everton have assembled a list of targets in addition to the trio. Former Croatia and West Ham manager Slaven Bilic, who had a short spell as a player at Everton, and former Borussia Dortmund coach Lucien Favre have also been touted.

Everton owner Moshiri and chairman Bill Kenwright are leading the pursuit of a new manager and initially had hopes of making an appointment before the Villa game.