The report state that Besiktas are preparing a €3.5 million deal for the Liverpool player and that Sampdoria are also interested in the 24-year-old.
The Black Eagles are preparing a shortlist of targets of strikers following reports linking Demba Ba with a €14 million move away from the club.
The Mirror have suggested that Liverpool are keen to offload Balotelli this summer following a disappointing season.
Balotelli joined Liverpool from AC Milan for €20 million but has managed to score just four goals in 28 appearances.
The 24-year-old has previously played for Manchester City, AC Milan, Inter Milan and Lumezzane.
Balotelli also has 13 goals in 33 international appearances for the Italian national team.
Besiktas finished the Turkish Super Lig season in third place and will compete in the Europa League next season.