The Red Devils have already seen a joint £28m offer spurned by the Merseysiders, who were offended by the figure put forward by their former boss.
It has been speculated that Moyes – who slammed the club he left earlier this summer for refusing to sell – will return with an improved bid, but this may well be rejected once more.
If this proves to be the case, the Scot will only move for Fellaini.
The burly Belgian appears to be the more realistic target, with reports claiming he is desperate to swap Goodison Park for Old Trafford.
Moyes believes that Everton boss Roberto Martinez may be happier to part with Fellaini than Baines, as he is believed to be interested in Wigan’s defensive midfielder James McCarthy.
As it stands, the Spaniard cannot afford to raid his former club unless he makes at least one big sale.
Baines was said to be Moyes’ main target, but with the full-back having not pursued a move he is said to willing to back off.
United may instead turn their attention to Southampton’s teenage sensation Luke Shaw next summer.
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