Speculation over Mourinho's future in the Spanish capital has been well-documented since Tuesday night's elimination at the hands of Borussia Dortmund in the Champions League semifinals.
Valdano, who worked alongside Mourinho for a period before a public spat between the two saw him leave the club, is certain things will carry on as usual at Madrid even if the Portuguese coach does move on.
"Real Madrid are still an extraordinary side. From this point of view, it will not matter if there is a change in coach," Valdano told Cadena Ser. "Real Madrid are a very big and complex club, there are thousands of people behind the scenes."
Asked what coaches he thought could replace Mourinho, he said: "[Carlo] Ancelotti is a great man, he is diligent, calm and has the capacity to create something special. He has the ability to work naturally even under controversial conditions.
"But, I admire [Jurgen] Klopp a lot. He has the optimism that can bring his team joy.
"German football and Bayern Munich know where they want to go. They are doing so with a great style of football."Valdano also touched on how los Blancos almost overturned the deficit against the Germans in Tuesday's night game.
"Coming back is part of Real Madrid's fabric," he added. "It's part of its image and it's very impressive. Barcelona are different, they have great faith in their philosophy, but they do not have a history of coming back in the big ties."