The Daily Express says the champions will return for the 28-year-old in the New Year.
Everton manager Roberto Martinez has praised his left-back as among the worlds best, but with his current contract set to expire in 2015 his future at Goodison Park is far from certain.
Martinez had suggested a new deal would be handed to Baines in the wake of his loyalty to the Merseyside club, but admitted last month no talks had taken place.
And United boss David Moyes is now preparing to take advantage of Everton's hesitancy after placing Baines at the top of his January shortlist.
For breaking stories and all the great banter like us on Facebook: facebook.com/tribalfootball