The Black Sea based side have been closely linked with the Moroccan international since appointing Süleyman Hurma as sporting director.
Hurma was responsible for signing Amrabat to Kayserispor from PSV and selling him to Galatasaray for €8 million.
The former Kayserispor sporting director has close ties with the 28-year-old winger and is reported to be close to reaching an agreement.
Amrabat spent last season on loan at Malaga. The La Liga outfit had a clause to sign the Moroccan international on a permanent basis but were unable to match Galatasaray’s asking price.
Galatasaray manager Hamza Hamzaoğlu did however, recently reveal that he wants to keep hold of Amrabat.
“I do have plans for Amrabat next season,” Hamzaoğlu was quoted as saying by Lig Tv on his signing ceremony.
West Ham and West Brom are also reported to be interested in the 28-year-old winger according to Talk Sport.