The Turkish league winners are searching for a new goalkeeper following the departure of Fernando Muslera.
The Turkish side are looking to bolster their squad for next season after winning the league title.
Galatasaray make move for Alisson
Galatasaray is interested in acquiring Alisson, who is under contract with Liverpool for two more years.
According to Sky Sports Germany, Galatasaray has expressed interest but hasn't made a formal approach.
The Brazilian goalkeeper has made it clear he has two years remaining on his Liverpool contract and is fully committed to the club.
Alisson joined Liverpool in the summer of 2018. Since then, he has won two Premier League titles, a Champions League title, an FA Cup, and two League Cups.
He has made 298 appearances for Liverpool, keeping 127 clean sheets.