The Sunday Sun reports that the Red Devils are keen to move in for the England international left back.
David Moyes had a joint bid for Baines and Fellaini rejected last August and decided at the time to focus his attentions on signing the latter.
Having secured the Belgian international on transfer deadline day, Moyes is now thought to be keen on making Baines his number one transfer target at Manchester United in January.
Roberto Martinez is reluctant to let go of one of his star players in the winter yet could be persuaded to let the 28 year old leave in a part exchange deal.
The current boss at Goodison Park managed the player at his previous club Wigan before selling him onto Everton for £6 million.
Baines has been in imperious form for the Toffees so it is thought that he would now fetch in the region of £20 million outright but moving Zaha in the opposite direction could knock down this fee and make the deal affordable for both clubs.
Manchester United have currently won their last 4 Premier League games in a row and look to have built some momentum ahead of their title clash with Arsenal this weekend.