The Red Devils were heavily linked with the England international over the summer, but David Moyes was unable to persuade his former club to let his one-time star player follow him to Old Trafford.
Despite the rejection, the Scot has remained keen, and is ready to take full advantage of Baines’ current contractual uncertainty.
The defender’s deal will enter its final 18 months at the turn of the year, which could leave the Merseyside club at risk of seeing his value decrease rapidly.
United are hopeful that a fresh £20m offer for the 29-year-old will be accepted by the Goodison Park outfit, who are growing aware that their star man could leave for free in the not too distant future.
The Premier League champions’ two offers for Baines during the last window were deemed to be below his worth, and Everton boss Roberto Martinez says that they will continue to hold firm until their valuation is met.
“My answer is clear. When I want a player I need to understand the valuation. If I really want a player then I need to match that,” Martinez said.
“Then I put the other club and the player in a situation to decide. That’s not happened. We have never been in a position where the valuation has been matched for Leighton.
“We don’t need the money. We don’t need to balance the books. And that’s something we wanted to have.”