United are unwilling to increase their bid of £16million for the Argentina defender, with reports in Portugal suggesting Sporting may accept that amount if a United player goes in the opposite direction on loan.
Sources suggest Rojo is unlikely to play for Sporting again. He was suspended by the club after refusing to train last week, and missed the club's league match on Saturday.
Rojo is now expected to make the move to Old Trafford but if the deal does fall through, United will turn their attention to Stuttgart's Antonio Rudiger.
Sporting have been holding out for more for Rojo as they only own 25 per cent of the player.