Mourinho is the red-hot favourite to be appointed as the Blues' new manager with his summer exit from Real Madrid confirmed earlier this week.
Former Germany captain Ballack played under the Portuguese during his first spell at the helm of the West London club from 2004 to 2007.
And the midfielder, who spent four years with the Premier League club after signing from Bayern Munich in 2006, believes Mourinho will be able to lift the star-studded squad to new heights.
Ballack said: "Going back to a club where the fans love him, the club loves him but also English football loves him (could be good).
"He is special and brings this little bit extra off the pitch as well. That is part of football today.
"If you see his success in club football over the last few years, it is fantastic. From my point of view, I can say I really enjoyed working with him in the two years. He was really professional."
Ballack does not believe Mourinho has anything to prove after his stint with Real Madrid, having already lifted the European Cup during his time with Porto and Inter Milan.
He added: "He is still young as a coach. He already won two Champions League finals. Not winning with Real Madrid, of course, is a disappointment for the club.
"But he showed he can do it with other clubs as well. That is why maybe he is now looking for a new challenge.
"I do not think he has to prove anything anymore.
"But for yourself as a person, you want to prove all the time. You want to win every game and that is what makes it so special and difficult.
"Around the media, the expectations are a part of football. I think Mourinho can handle it."
Michael Ballack is an adidas ambassador and was speaking at the launch of the adidas lab - a showcase of the latest adidas football innovations including the world's lightest football boot. Join the conversation @adidasUK #adidaslab