Rojo was signed by Manchester United after the World Cup in Brazil in 2014.
The Mail reports that Rojo was close to leaving Old Trafford in the summer, with Ligue 1 side Monaco said to have shown strong interest in the Argentine but a deal could not be agreed.
West Ham United's Dimitri Payet in action with Manchester United's Marcos Rojo and Ander Herrera
He has made a total of 12 appearances so far this season in all competitions - both at left-back and at centre-back - while he has been playing in the latter role for Jose Mourinho's side in each of United last four Premier League games.
The report goes on to say that Mourinho would like to sign a new centre-back in the January transfer window, and that selling Rojo could make room for a new arrival.
However, United have been hit with injuries at the heart of their defence with both Eric Bailly and Chris Smalling currently on the sidelines.
Manchester United's Marcos Rojo
Rojo has partnered both Phil Jones and Daley Blind at centre-back so far this season, and one would question whether it would be the right time for Mourinho to let a defensive option depart - especially with Bailly expected to be part of the Ivory Coast's squad for the Africa Cup of Nations.
United would be looking to recoup close to the £16 million they paid Sporting (BBC Sport) for Rojo back in the summer of 2014 should a deal be struck.
West Ham United's Mark Noble, Manchester United's Marcos Rojo and referee Jonathan Moss