The daily paper claims that Balotelli has been offered to the Istanbul based club after the Red’s boss Brendan Rodgers dropping him from the squad.
AMK also state the Galatasaray are only willing to take the Italian international on loan with the option to sign him at the end of the season.
The Italian international has however, been frozen out of the Liverpool team after a training ground dispute according to the Daily Mail.
Balotelli has fallen behind the pecking order with Christian Benteke and Danny Ings joining over the summer transfer window.
The 25-year-old joined the Reds on a £16 million transfer last season but struggled to settle in and failed to score a single goal.
Liverpool won their second game of the season 1-0 against Bournemouth last weekend.