The game against Osasuna was Mourinho's last in charge of Real but neither Chelsea nor the coach have yet confirmed his next destination.
Former Portugal centre half Carvalho played under the coach when Chelsea won back-to-back Premier League titles in 2005 and 2006.
Asked by Sky Sports television if Mourinho could win the Premier League again at Chelsea, the defender replied: "I'm sure in two, three years they can but even in his first year he can win it again.
"When we arrived together in 2004 Chelsea had not won the league for 50 years so I hope now they can win it again. Jose is a special coach and I think he deserves all the best because he works very hard.
"Chelsea are a special club for me and I wish for them to win the Premier League again."
Carvalho, 35, played for the Londoners for six years, making 181 appearances and scoring 10 goals before joining Real in 2010.
He is now a free agent and has already agreed to join newly-promoted Ligue 1 club Monaco next season.
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