The centre-half described Mourinho as the “best coach in the history of football” having played twice under the Portuguese manager.
“If it were possible to sign for Real Madrid, I will go there immediately, swimming or running,” Carvalho told AS.
“It would be a dream to play for Madrid, which I regard as the best club in the world, and be under the command of the best coach in the history of football,” he said.
The 32-year-old was brought to Chelsea by Mourinho in 2004 after winning the Champions League under the Portuguese coach at FC Porto.
“Being able to win another Champions League with Real Madrid would be fantastic,” added the defender.
Mourinho took over at the Santiago BernabÃƒÂ©u following Manuel Pellegrini’s sacking in May.
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