Toffees want Scot’s successor in place before the start of pre-season.
Everton have made highly-rated Swansea City head coach Michael Laudrup their first choice to succeed current manager David Moyes, who is expected to be confirmed as the new Manchester United boss on Thursday, reports the Daily Mirror.
Laudrup, 48, is contacted to Swansea until 2015 and so it may prove problematic to be able to persuade the South Wales club to allow the Dane to leave the Principality this summer.
The former Real Madrid, Barcelona and Juventus player, however, has enjoyed an outstanding debut campaign in charge of the Premier League minnows, guiding the club to a mid-table league finish, as well as to their first-ever piece of silverware when Swansea beat Bradford City to win the Capital One Cup at Wembley last February.
Laudrup has been in charge of the Swans for 45 matches in all competitions to date this season, winning 17 and losing 13 of those contests to give him a win percentage of just 37.