Former Manchester City boss Mancini was appointed as Fatih Terim's replacement at the Turk Telekom Arena on Monday after Terim paid the price for a poor start to the season that yielded just one win in five Super Lig matches.
Terim also oversaw the humiliating 6-1 home defeat to Real Madrid in Galatasaray's Champions League Group B opener, as Cristiano Ronaldo stole the show with a second-half hat-trick.
And the club have now turned to Mancini to reverse their fortunes, although the Italian could hardly have asked for a more daunting first game as he takes his new side to his homeland to face the Serie A champions.
Galatasaray head into the fixture at the Juventus Stadium on Wednesday on the back of a 1-1 draw at home to Rizespor. Engin Baytor opened the scoring, but Tevfik Kose levelled in the second half before Selcuk Inan saw red.
Midfielder Hamit Altintop continues to be plagued by a hip injury and is likely to miss the visit to Turin.
Juve, meanwhile, will be desperate to claim maximum points after a disappointing 1-1 draw away to Copenhagen in their opening fixture.
Antonio Conte's team are in good form ahead of Wednesday's showdown, and are on an eight-game unbeaten run in all competitions.
They will look to build on the momentum from their 1-0 victory over rivals Torino at the Stadio Olimpico on Sunday, with Paul Pogba's second-half header securing the points.
The France international has now set his sights on the Champions League, and said the side are itching to atone for their surprise draw in Denmark.
Speaking to Tuttosport, he said: "We know it will be an important match for us, we have to win it and we know it won't be easy.
"I don't know if it will be decisive for qualification, but after the draw with Copenhagen we all want to win."
Juve could be without influential striker Carlos Tevez after he picked up an ankle injury against Torino following a robust challenge from Ciro Immobile.
The Argentinian has notched three times in Serie A since his transfer-window move from Manchester City, where he played under Mancini.
