The Argentina international only signed a new deal with United back in March, but has been told by the Reds he is free to leave, with Everton now weighing up a move.
United paid Sporting Lisbon £16 million for the player for years ago and are now willing to cash in for £20 million, a figure that Everton would be willing and able to match.
However, reports have suggested that Rojo is on £120,000 a week at Old Trafford and the Toffees are not willing to smash their pay structure to get him on board.
What is does mean is, Rojo would have to take a big pay cut to complete the move, something he may not be willing to do while other clubs are interest.
Everton boss Marco Silva is keen to bolster his defence, but unless Rojo lowers his demands, a move looks unlikely.