By FOX Sports Staff
Mourinho is yet to confirm reports in England that he has penned a £40million four-year deal to return to Stamford Bridge since his sudden exit in late 2007.
What is known is that Saturday's 4-2 win over Osasuna at the Bernabeu was his last game in charge of Real Madrid.
And Real defender Carvalho, who is set to join Monaco in the summer, has no doubt his fellow Portuguese will bring back domestic success to Chelsea after a mini trophy drought in the Barclays Premier League.
"I am certain that Jose can bring the good times back for them," said the 35-year-old in a post-match interview.
"He did it when we first went there in 2004 and he will do it again in 2013.
"For the last two years Manchester United and City have been at the top of the league in England.
"But I'm sure Chelsea will improve when Jose goes back there. It's important for them to win the Premier League again and, with Jose in charge, they will do that."
Chelsea have not won the Premier League title since Carlo Ancelotti's Blues did the double in the 2009/10 campaign.
Mourinho has not spoken about his next step yet but did issue a thank you message to the club's supporters prior to Saturday's victory.
"I wish everyone associated with Real Madrid much happiness in the future," he was quoted on the club's website as saying.
"I appreciate the support of lots of fans and respect the criticism of others.
"Once again, a lot of happiness to everyone and, above all, good health. Hala Madrid!"
Mourinho's era at Real fittingly came to an end in a divided Bernabeu with sections of the stadium singing his name throughout the 4-2 win over Osasuna, while other sections responded to the support with boos and whistles.