And Mourinho admits it is an honour for him to be linked with a shock return to the Spanish capital in the future.
It does suggest that Mourinho actually stands a chance of returning to Santiago Bernabeu, and reports over the last few days have even suggested they moved for him following Lopetegui's dismissal - and while he was still at United.
The improved contract United agreed with Mourinho a year ago was due to run until the end of the 2019-20 season, with an option of a further season.
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.More news: Far-right German politician seriously injured in gang attack
Mourinho's first fully-fledged job as a manager was with the Eagles where he took over from former Bayern Munich boss Jupp Heynckes in 2000.
Their 2-0 home defeat by Real Sociedad on Sunday saw them slump to fifth in La Liga, 10 points behind leaders Barcelona.
He said on the prospect of returning: "They are things that are said and I will not feed".
In his first TV appearance since leaving Manchester United in December, the former Chelsea, Real Madrid, Inter Milan and Porto manager will be part of a panel of expert analysts based in beIN SPORTS' studios exclusively covering two of the most watched products in the MENA region.More news: Australian police arrest man over suspicious packages sent to embassies and consulates
Solari's job is now under huge threat and reports in Spain claim Real chiefs want to bring back Mourinho to save their season.
"When a professional returns or is invited to return to a club, it's a great honour".
A source close to Mourinho revealed on Wednesday night: "There are no issues over Jose's contract with Manchester United". It's not a gamble in the dark, the clubs are trying to hire a player or a coach they know because they've already been there.
Manchester United have said that they are not preventing their Ex-Manager from joining any club.More news: Phillies rumors: Expect Manny Machado decision in the next week
Benfica's previous coach, Rui Vitória, left by mutual consent last Thursday with the Lisbon club third in the league and has now taken over at the Saudi club Al-Nassr.