Mourinho is said to have rejected the chance to return to his former club, deeming it too early in his career for a return to Portugal.
"There are no issues over Jose's contract with Manchester United".
The source explained that Real sounded out Mourinho prior to Solari's hiring, with the Portuguese boss stating his commitment to his job at Old Trafford.
Jose Mourinho has only been out of a job for a few weeks, but he is already set to return to our television screens.
Jose Mourinho will join beIN SPORTS, the global sports broadcaster, this week as part of the AFC Asian Cup 2019 and English Premier League coverage, which viewers across the Middle East and North Africa (MENA) enjoy exclusively on the leading sports channel.
It was never going to be an easy season after both Zinedine Zidane and Cristiano Ronaldo left but Julen Lopetegui had a nightmare time before being replaced by Santiago Solari.
According to the publication, Real boss Florentino Perez remains a huge fan and the Champions League holders will do all they can to land the manager.
Their 2-0 home defeat by Real Sociedad on Sunday saw them slump to fifth in La Liga, 10 points behind leaders Barcelona.
"When any professional returns to a club it is a tremendous honour".
Mourinho is sure to have plenty to say about the game featuring another of his former clubs, as well as a team he has not held in the highest esteem during his time in English football.
But the manager was let go by the club due to their struggles in all competitions this campaign as they were sixth on the log before he was sacked.
The source added: "There has been no contact, but they did get in touch with Jose after Lopetegui was dismissed, but he told them he was the manager of Manchester United and totally committed to the club".
Mourinho has also been spoken of as a possible successor to the axed Rui Vitoria at Benfica.