El Pais claim Real Madrid sounded out Mourinho to return to the club next season but were told he had the pre-contract agreement with United.
Mourinho has been constantly linked with a move to Old Trafford since his sacking as Chelsea manager in December.
In February, a friend of the former Inter Milan boss confirmed that he was destined to replace Van Gaal at the Premier League club.
Inter director Bedy Moratti, sister of the Italian club's former president Massimo Moratti, divulged the news after having lunch with Mourinho and her family in the city.
Asked afterwards if the 53-year-old Portuguese coach will return to Inter, she replied: 'No, he's happy now, he's going to Manchester. Of course, he's always fantastic and we missed him as a person here.'
Mourinho recently stressed that he is keen to return to management this summer.
Speaking in Singapore last month, he said: 'I always feel that it's better to wait, not to rush, better to be calm, to wait for the right moment, the right move.
'I feel that starting the next season with a new club and project is probably the best thing for me.
'It's quite a funny career. I am the English champion, and I still have no job.
'I read so many different things. One day it says I go to China, another day it says I go to Italy, and people say I'm back to Inter Milan. I'm here - probably, you are saying I will go to the Singapore national team.'
United have struggled to find an identity under Van Gaal, whose position as manager has been the subject of intense speculation for several months.
The Red Devils currently lie sixth in the Premier League table, four points off the Champions League places, and were knocked out of the Europa League by Liverpool at the quarter-final stage on Thursday.
Van Gaal has frequently leapt to the defence of his record at Old Trafford but the rumours linking Mourinho with a move to Manchester as his replacement have never gone away.
- Daily Mail
