The report claims United submitted a £15m offer for the England international today - the first time they've separated out an offer for Baines distinct from a joint bid with Marouane Fellaini.
But Toffees chairman Bill Kenwright remains adamant that Baines will not be allowed to leave Goodison Park this window.
United boss David Moyes, who managed both Baines and Fellaini at Everton, had a £36m joint bid for the pair rejected earlier this month.
But the report claims he's gone back in for the left-back, only to be told that he is not for sale.
Speculation continues to link Fellaini with a move to Old Trafford, with the Belgian FA confirming via Twitter that he will not train with his international teammates on Monday - he will join up later.
The tweet did not give a reason for the delay - but it could have something to do with interest from David Moyes.
Manchester United also continue to be linked with a late move for Athletic Bilbao midfielder Ander Herrera.
Reports today claim the Premier League champions are willing to match the 24-year-old's €36m buyout clause, but United face a race against time to beat the deadline.