He also called for the club to sign Paris Saint-Germain midfielder Vítor Machado Ferreira, known as Vitinha.
Speaking to Radio Marca, Guti delivered a wide-ranging verdict on a club he played for 542 times between 1995 and 2010 that is facing its most turbulent period in decades — two consecutive years without a trophy and a dressing room rocked by the Valverde-Tchouaméni incident.
"Mourinho is a great, great coach and could do things well at Real Madrid."
He stopped short of advocating a straight appointment, insisting the problem runs deeper than whoever sits on the bench.
"It's two years without winning anything. There must be more problems inside the club than just the name who is sitting in the dugout. The problem at Real Madrid is not Vinícius, not Jude Bellingham, not Kylian Mbappé. The problem is the team. When you have a good squad you fight for everything — when you don't, it is harder to compete for a long competition like La Liga."
On Mbappé, who drew criticism for travelling to Italy for personal reasons before the Clásico, Guti was protective.
"As long as they do things right on the pitch, what they do off it doesn't matter to me. In their personal lives, everyone does what they want."
He added he hoped the French forward would be available on Sunday.
"Hopefully he makes it because he can contribute so much to Real Madrid."
His most pointed footballing opinion was reserved for Vitinha, the 26-year-old Portuguese midfielder who has been one of the driving forces behind PSG's Champions League campaign this season.
"In Spain, Pedri is above everyone — he is the best midfielder there is. At a global level, Vitinha is one of the most complete midfielders there is. The best players should be at Real Madrid and Vitinha is the best at his position."
On his own club's youth policy, Guti was direct.
"It should be a club policy to invest in the academy. Arbeloa is doing good work with the young players."
Spain's World Cup prospects, he said, rested on the shoulders of Barcelona midfielder Pedri and the collective experience of the squad. He was particularly positive about the presence of Real Madrid captain Dani Carvajal among the group.
Vitinha's PSG contract runs until 2028. He said in March he has no desire to leave Paris. Guti's endorsement may not change that — but it will keep the conversation alive.