The Argentine defender moved to Old Trafford from Sporting Lisbon back in 2014, but has struggled to win over fans after his disappointing performances in the Premier League.
He has been in action for Argentina at the Copa America and has been deemed a surplus to requirements by the Portuguese boss at Old Trafford.
Man United are reportedly prepared to take a financial hit and accept an offer of around £10million with clubs from China, Italy and Spain interested in signing him.
Louis van Gaal signed Rojo after his impressive performances against Holland at the 2014 World Cup, but he has failed to live up to his potential and could be on his way out of the club.
Mourinho has already signed Eric Bailly and will be looking to offload players this summer before he heads into his first season in charge at Old Trafford.
There has been plenty of speculation linking Mourinho with another defner and he could be looking to bolster his side’s defensive options before he let’s the Argentinean leave the club.