The Red Devils are understood to have intensified their search for a new defender since their opening day loss to Swansea, with the Argentine the main man on their list.
It’s understood that a bid for Rojo was made last week, but Sporting are reluctant to sell for under £20m, despite the intervention of the player’s third party owners.
But Sporting may be willing to accept an offer of around £17m if Nani is included.
The winger signed for United from the Lisbon giants in 2007, and has endured a largely underwhelming spell at Old Trafford.
Sporting are eager to get him back, and Louis van Gaal may sanction such a deal with the player unlikely to have much of a future in his 3-4-1-2 set-up.
United are also looking at Mehdi Benatia of Roma, while rumours suggest that Arturo Vidal, a defensive midfielder, remains on their agenda despite lengthy negotiations.