The Premier League outfit are reported to have joined the race for the on loan Malaga player.
Malaga have expressed an interest in making Amrabat’s temporary stay permanent and will hold talks with Galatasaray at the end of the season.
Sevilla and Olympiakos have also been closely linked with the Moroccan international.
The Morroccan international joined Galatasaray on an £8 million move from Kayserispor in 2012 and still has two years left on his contract.
The 28-year-old has been in impressive form at Malaga and has four assists and five goals in all competitions this season.
The La Liga outfit have a €3.5 million buy out option which runs out in May 2015.
Amrabat was named in Marca’s October La Liga Team of the Month.