Prandelli resigned as Italy's national team manager after the team failed to get past the group stage at the ongoing World Cup in Brazil.
Former Inter Milan and Manchester City manager Mancini left Galatasaray this summer after less than a season at the Istanbul club, when they lost the championship to arch rivals Fenerbahce.
"Galatasaray Sportif has announced that they have begun negotiating with the Italian football manager Cesare Prandelli," the club said on its website.
"The public will be updated about further developments."
Media reports had also linked former Everton and Manchester United manager David Moyes as a candidate for the post.
(Reporting by Ece Toksabay; editing by Sudipto Ganguly)
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