The 26-year-old has risen to become one of the best 'keppers in the world during his six seasons at Old Trafford, and could fetch a whopping £60m if he moves to the Bernabeu this summer.
He said: "I can't say any word about a player who is a Chelsea player, I can't, it's hard, it was a little bit of the same with Morata, we have to respect the player, the club, the owner, the manager, I don't want to be disrespectful, and be speaking about the player". "I am nobody to speak about players from Real Madrid", Mourinho said.
"Yes, we have had interest, that is obvious and it's public".
"They've identified for a long time that his development at Juventus, his training at Madrid and the fact that he's a consistent trophy victor at a very young age, meant that they thought he was the right player".
"But it's a Real Madrid's right to ask for their players the amount of money that they want".More news: BigBoss' Tamil version row: Hindu Makkal Katchi protests outside Kamal Haasan's residence
"I would not like to be in [chief executive] Ed Woodward's position negotiating because everything is really hard", Mourinho told reporters ahead of United's first pre-season friendly against MLS side LA Galaxy.
Both Juventus and United are linked with Matic so there is more than one club interested in him but United signing Romelu Lukaku from under Chelsea's nose raises a question of whether Antonio Conte will even deal with United and strengthen a title rival.
"The directors made an offer which they felt was fair but even so, we didn't reach an agreement". However, the Old Trafford club were successful in beating the Blues in signing the Premier League striker.
Transfer market expert Graham Hunter says striker Alvaro Morata should sign for Chelsea this summer. AS says the English champions will submit a €80m (£70.2m) bid for the Champions League and La Liga winning striker as Conte looks to bolster Chelsea's attack for the new season.