The Spanish side are looking to get their season back on track and have allegedly identified Rojo as a main target to avoid entering the relegation zone.
He has become a vital member of Jose Mourinho’s squad in the last few months, starting the last eight games in a row, that has seen United remain unbeaten in the Premier League.
Reports claim Valencia sporting director Jesus Garcia Pitarch has been in England to discuss a potential switch in the January transfer window.
United have already thought to have knocked back interest in his services, but with Benfica centre-back Victor Lindelof said to be arriving next month, they may need to offload some players.
Valencia have endured a horrible start to the season so far, earning just 12 points from their 15 games.
Although he has been heavily criticised at times, he has massively improved his game under Jose Mourinho and has become a solid player at the centre of defence.
Rojo has racked up 72 appearances in all competitions since he joined United from Sporting Lisbon in a £16m deal in 2014 and a transfer could see his short career at the club come to an end.