The pair have history, with the legendary Italian boss having tutored the former forward while at Juventus in 1993, and even clashed following a pre-season game when the striker pushed the manager over after just five minutes of a close-season friendly.
But, the 74-year-old believes his former charge has matured from the "abrasive and confrontational" nature of before and will now make a fine head coach at the Stadium of Light.
"Paolo was a fantastic, creative player and as a player he was a little bit strange as I discovered when I was his manager," Trapattoni is quoted as saying by the Daily Mail.
"He can be a good manager now because he will have learned how to deal with players. When he went to England to play it gave him more experience.
"I know he was in Rome a long time ago, it is the capital and it is a different place for him and he is very proud to come from there.
"But England was also a different place for him and a new experience in his life and he matured there and he grew. It was a different situation for him and he changed there for sure.
"I wish him well and wish to give him my congratulations that he has become a manager.
"He was abrasive and confrontational as a player and I saw that but that is his character. He can be a good manager, I am sure."