Moyes is said to be targeting a £40m double raid on his former club for left-back and England international Leighton Baines and Belgian midfielder Maroune Fellaini.
Baines comes with a £17m price tag and Fellaini has a £23m buyout clause in his contract. The 25-year old midfielder was a target for Chelsea, but the lure of linking up with his previous manager could be influential in his summer decision.
Moyes was confirmed as replacement for the retiring Sir Alex Ferguson yesterday after the 71-year old Scot stepped down from 26 years at the helm of the Manchester Club.
Moyes will take over on July 1 after taking charge of Everton for their last two matches of the season, and their last home game this Sunday against West Ham.
Moyes has been at the Merseyside club for 11 years.