But the Red Devils manager doubts a move would ever happen as it is almost prohibited for Real Madrid to sell the Portugal forward.
United signed Ronaldo from Sporting Lisbon in 2003 and he quickly established himself as one of the most talented players in the world.
He was sold to Real nine years ago, but not before he won three Premier League titles, the FA Cup, League Cup and Champions League under Sir Alex Ferguson.
Ronaldos reputation continued to soar after joining Real – he now has four Champions League medals and is the owner of five Ballon dOr awards.
The 33-year-old encountered his first problems in the Spanish capital last summer and was linked with a stunning return to Manchester United.
But Mourinho believes Real Madrid cannot sell Ronaldo, despite admitting he is a player who would always be welcome back at the Theatre of Dreams.
I believe that Real Madrid cannot sell him, it is prohibited, Mourinho told Portuguese newspaper Record.
He has to stay until the moment they authorise him to go and play one year in America or anywhere else that he wants to enjoy. It is a closed door.
Asked about Manchester Uniteds interest in the superstar forward, Mourinho added: I dont think so.
But all the people know his history in Manchester, the passion they have for him and that there are players in the world who, if the clubs have the possibility of signing, will not say no.
Mourinho also opened the door to becoming Portuguals national team coach after his reign at Manchester United ends. The 55-year-old says he considered the role while at Real Madrid.
I almost went once, but [Real president] Florentino Perez didnt let me, because he thought that the position of Real coach was not compatible with the national team, he said.
[Ill consider it] only when Im tired of the day-to-day, the three matches a week, the seven training sessions per week, and the one month pre-season, things that dont tire me now.