
Ferguson, 71, revealed his decision to step down on Wednesday after nearly 27 years in charge at Old Trafford.
Fellow Scot Moyes, in charge at Goodison Park since 2002, held talks with Toffees chairman Bill Kenwright on Wednesday evening.
Kenwright told Sky Sports News: "At the end of the day, David's contract is up in six weeks' time and he has a right to make his own decisions. He has served this club wonderfully well."
Real Madrid boss Jose Mourinho has also been linked with the task of replacing Ferguson but Moyes looks set to get the job.
Wigan's Roberto Martinez and Swansea's Michael Laudrup are thought to top Everton's list of potential replacements should Moyes, as expected, be confirmed as United's next manager.
The Scot, 50, is expected to tell Everton players and staff of his decision to join United at a training ground meeting on Thursday morning.
/BBC/