Leon Osman, Leighton Baines and Marouane Fellaini were Moyes’ talismans at Goodison Park, and were the Toffees stars linked to the Red Devils.
Osman has signed a new deal with Merseyside club however, leaving Baines and Fellaini as the likeliest targets for United.
According to a report on The Guardian, Baines is not blinking brightly on United’s transfer radar.
Fellaini however, is a different matter.
Although Moyes often deployed him as a secondary forward, the rangy Belgian is a natural central midfielder.
He specialises in the position that United most glaringly need to reinforce.
"I'm not a No10," Fellaini said last week.
"David Moyes predicts my future as a defensive midfielder, but due to a lack of offensive power, he plays me up front. In the future I want to play as a 6 or an 8. From there I can create danger and score goals."
Michael Carrick, youngster Tom Cleverley and veteran Ryan Giggs are the English champions best nominative central midfielders at the moment.
Paul Scholes has retired again, Anderson is in a malaise and Darren Fletcher’s chronic bowel disease means he is not expected to play again anytime soon.
As a result, Fellaini has been pegged to fill a hole in United’s midfield.
He enjoys a healthy working relationship with Moyes, who has been informed that Fellaini’s £24 million buyout clause is within reach if the player is needed at Old Trafford.
Fellaini has often been non-committal regarding his long-term future with Everton, and recently said that if he were to leave, it would only be for a manager “who really wants me.”
There has been no comment from either United or Everton regarding the mounting rumours that Fellaini could be Old Trafford-bound.
But as far as transfer silly season goes, you are unlikely to hear a more logical rumour, whether it comes to fruition or not.