The Ivorian legend has been widely linked with a move to Turin after helping the Turk Telekom Arena club to the Super Lig title and the Turkish Cup during an 18-month spell at the club.
Mancini believes that the Italians would do well to sign him as they look to retain domestic hegemony and make a bid for the Champions League.
"If Juventus were to take Drogba, it would be a great signing," he told Tuttosport.
"He'd be an important reinforcement, very useful, particularly in order to have an assault on the Champions League. Drogba can give you a lot from this point of view.
"I've trained Drogba this season and it was a pleasure to do so. He's a great champion. I can tell you that I was amazed by Drogba - he's a great person.
"He always behaved well with me, from the first minute to until the last. His contribution was never limited to the pitch alone.
"If anyone thinks he is not as motivated as before due to his age, they're wrong. After all these months I can confirm that he's decent, driven and humble.
"He can't play 50 games a year, of course. Time passes for everyone, even him. But even when he's not 100 per cent, he's still devestating to opponents.
"He hasn't played for the last two months, but he's preparing for the World Cup and I know he is already much better."