The West Brom manager worked with the Portuguese during his time at Chelsea, forging a strong bond, and believes that his old boss has proved his quality with los Blancos' recent results.
"When you look at his track record and the clubs he has been at, [Madrid] is one of the clubs he could manage," Clarke told reporters.
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"Over the Christmas period, they definitely had a rocky patch where it looked as though things weren't going to go great for Jose but they have turned it around quite well. They have beaten Barcelona twice and now turned over Manchester United."
Mourinho's side knocked the Red Devils out of the Champions League on Tuesday and Clarke says that the 50-year-old is fixed on securing his Madrid legacy by claiming 'La Decima'.
"I am sure Jose is focused on the fact he is going to try to win the Champions League with a third different team and in a third different country," the Baggies boss added.
"I think that would be his main aim now and he will be completely focused. He is under contract with Real Madrid.
"As and when Real Madrid decide what they are going to do with their coach towards the end of the season, that becomes a different question."