The former Spain international has voiced his admiration for the Portuguese coach, and has praised the development of players such as Ronaldo, Benzema, Di Maria and Higuain
Butragueno has praised the former Inter boss for his leadership skills, and believes Mourinho's experience will give the team an extra edge in the tail end of the season.
"We have a coach who is a great leader. He is used to winning titles. He knows exactly how to harness all the different personalities a big team like Madrid contains," Butragueno stated to uefa.com.
"That keeps us calm, and now we are coming into this critical stage of the season, having a coach with all his experience is a great advantage."
Butragueno then went on to stress that Madrid have made significant progress in the past two years as several key figures have matured.
"Players like Karim Benzema are much more mature than they were two years ago. Angel Di Maria has helped us a lot, and Gonzalo Higuain has become a stable presence in the team.
"Cristiano Ronaldo understands the philosophy of the club perfectly; he has also become more settled."
Real Madrid are currently leading La Liga by six points over Barcelona. Mourinho's men will take on APOEL in the first leg of the Champions League quarter-finals on Tuesday.
For the next 10 weeks, Goal.com will be publishing exclusive extracts from Luca Caioli's new book, Ronaldo: The Obsession for Perfection. Check out the first extract, published on Friday, which looks at the Portuguese forward's humble beginnings in Madeira. Don't miss it!