The report states that Galatasaray’s sporting director Cenk Ergun met with Rodgers representatives in London.
Galatasaray parted company with Hamza Hamzaoglu following a dispute with the clubs President Dursun Ozbek.
The former Akhisar manager signed a one-year deal worth $500,000 making him one of the lowest paid members in the squad and one of the lowest paid managers in the league but he still managed to win the league and Turkish Cup.
Galatasaray won the double for the sixth time in club history under Hamzaoğlu and earned the right to become the first Turkish club to wear the fourth star.
The former Turkish national team assistant manager also won the Super Cup at the start of the season.
Hamzaoğlu was sacked despite having another three-years left on his contract which was extended over the summer.