Carvalho left Real for Monaco last month.
He told chelseafc.com: "I still watch for results also. Mourinho knows I like the club and when we spoke in Madrid we would talk about it and he would in the hotels before games tell me the results of the games.
"He is a special coach for me. Last year I thought was not a happy one but this is the right move for him. He has the respect of everybody at Chelsea, the fans love him and the players know how he works. He is a great coach and gets results. Chelsea can improve their consistency in the league and I think he will do that."