The Turkish sports newspaper claims West Ham boss Slaven Bilic wants to bring the Senegalese international back to the Premier League.
Bilic oversaw Ba’s transfer from Chelsea to Beşiktaş last season and established a close working relationship with the powerful striker.
Ba scored a total of 27 goals in all competitions for the Black Eagles – a career high.
The 29-year-old striker has years of Premier League experience behind him having played for Chelsea, Newcastle United and West Ham United.
Ba scored seven times in 13 appearances for the Hammers four years ago helping keep the East London based side in the Premier League.
The Beşiktaş striker has also been linked with a €14 million move to Qatar but recently appointed manager Şenol Güneş has revealed that he wants his star striker to remain at the club next season.
Bilic was in charge of Beşiktaş for two seasons before resigning at the end of the season and replacing Sam Allardyce at West Ham.