The report goes onto state that the Black Sea based side are aiming to complete the transfer by the end of the week.
Talks between Trabzonspor and Galatasaray have been on-going in the past week with the Black Sea Storm reportedly setting aside €2.7 million for the Moroccan international.
Amrabat spent the season on loan at Malaga and the La Liga club have been trying to sign the Moroccan international on a permanent basis but have been unable to agree a transfer fee.
West Ham and West Brom are also reported to be interested in the 28-year-old winger according to Talk Sport.
Galatasaray signed the Moroccan international from Kayserispor for €8 million in 2012 and he still has two years left on his contract.
Amrabat had seven assists and six goals in 25 appearances for Malaga this season.