The Argentine defender has been rock solid at the back lately, despite looking out of favour at the start of the season after being slow to settle in England.
Rojo joined United from Sporting Lisbon in the summer of 2014, but has undoubtedly hit the form of his Red Devils career under Mourinho this season.
According to The Sun, this marked improvement could see his current contract extended by another year until 2020.
Mourinho has been happy with the 27-year-old’s performances, and hopes he’ll agree to new terms to keep him on at Old Trafford for longer.
Manchester United fixtures
West Brom (H) – Sat 1 Apr
Everton (H) – Tue 4 Apr
Sunderland (A) – Sun 9 Apr
Anderlecht (A) – Thu 13 Apr
Chelsea (H) – Sun 16 Apr
Anderlecht (H) – Thu 20 Apr
Burnley (A) – Sun 23 Apr
Man City (A) – Thu 27 April
Swansea (A) – Sun 30 April
Rojo is also said to be settled in Manchester and happy to talk over an extended deal with his manager.