Drogba confirmed the news on Sunday, bringing to an end his two-year stay in Turkey.
Mancini worked with the 36-year-old striker in the 2013-14 campaign as Galatasaray finished second in the Super Lig behind Fenerbahce, winning the Turkish Cup with a 1-0 success over Eskisehirspor in the final earlier this month.
Speculation in the media has linked Drogba with a move to Italian champions Juve, and Mancini reckons that would be a perfect fit both player and club.
"It would be a great signing if Juve were to get Drogba," he told Tuttosport. "I have coached Drogba this season and for me it has only been a pleasure to do it.
"He is a great champion. I can tell you I really have been surprised by Drogba. He is an extraordinary person.
"He has always conducted himself well for me, from the first to the last minute. He has been a tower of strength for my team this season.
"He would be a great and important reinforcement for Juve, especially when you consider Juve want to give the Champions League a good go.
"Drogba can offer a lot from this point of view. In Italy he can too, but especially in Europe. He is a leader, and for a coach it is vital to have those types of players."
