The Toffees are looking for a successor to Rafael Benitez after sacking the Spaniard on Sunday.
It has been reported that Rooney, the former Everton forward currently managing Derby, and ex-Chelsea boss Lampard are set to be interviewed for the post.
Having on Tuesday taken what was the team’s first training session since Benitez’s dismissal, Ferguson could be in caretaker charge when they host Aston Villa on Saturday.
The Scot, another former Everton player who has been part of their coaching staff since 2014, was caretaker manager for three league games in December 2019 following Marco Silva’s dismissal, a victory over Chelsea and draws with Manchester United and Arsenal.
Benitez, who replaced Silva’s successor Carlo Ancelotti last summer, was axed after Saturday’s 2-1 loss at Norwich left Everton with only one win and nine defeats in 13 Premier League games.
They are 16th in the table, six points above the relegation zone with two games in hand over 18th-placed Norwich.
Their search for a replacement for Benitez has seen Roberto Martinez, the Belgium head coach who was in charge at Goodison Park from 2013-2016, in the running.
It has been suggested Everton were prepared to consider Martinez combining the two roles until at least the summer but it is not a solution on which Belgium have appeared to be keen.
The Merseyside outfit were believed to be “putting out feelers” with a number of names to try to get an idea of potential interest and availability before drawing up a formal shortlist.
Everton academy product Rooney, who had two spells playing for the club either side of 13 seasons with Manchester United, has been in charge at Derby for just over a year.
The Rams’ battle for survival in the Championship this term after being deducted 21 points has seen them take 13 from the last 15 on offer – they are currently eight adrift of safety in 23rd place.
Lampard was Derby’s boss for the 2018-19 season, in which they were beaten play-off finalists, before taking charge at Chelsea in the summer that followed. He was sacked in January 2021 and has subsequently been out of work.
Everton are looking for a sixth permanent managerial appointment since owner Farhad Moshiri took over in 2016.
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