Toffees manager Ronald Koeman confirmed on Wednesday (26 July) that Barkley, 23, will leave Goodison Park this summer having rejected a lucrative new contract offer to remain at his boyhood club.
Everton placed a £50m price tag on the England international at the end of the 2016-17 season but that was before he decided to reject a new deal. With the club now so unequivocal in their plan to sell the player, that price is expected to drop.
The attacking midfielder is believed to be open to a move to Old Trafford that would see him follow in the footsteps of Romelu Lukaku, but the report adds Tottenham's interest remains stronger at this point in time.
Jose Mourinho is still hopeful of making a further two signings this summer with a defensive midfielder and a winger understood to be the two positions he wishes to strengthen most urgently. United are confident of signing Chelsea midfielder Nemanja Matic while Inter Milan's Ivan Perisic has emerged as the United's preferred choice to fill the wide role.
Barkley's availability however would appear to have prompted some interest, with Arsenal another club to have reportedly joined the race for his signature.
Speaking at a press conference on Wednesday, Everton boss Koeman made it clear under no uncertain terms that the England international would move on this summer, although the club had not received any official bids at that point.
"We made a good offer to him to sign a new contract, he declined that contract and told me that he's looking for new challenge. OK, he is not in Everton's future any more. It is his decision. I need to respect that and see what happens.
"What I heard from the board is that there is no offer on the table for Ross." When asked if he thought Barkley would '100%' leave Everton this summer, Koeman simply said: "Yes."