The 95-cap Japanese international joined Besiktas on loan in the January transfer window after making just four appearances for Borussia Dortmund.
A combination of injury and Lucien Favre’s preference to play Marco Reus as a central attacking midfielder meant he has become surplus to requirement at the club.
The 30-year-old has shown that he still has the quality left in him, after scoring three times in just two league starts for the Turkish club.
The report claims that Besiktas are keen to sign the former Manchester United attacking midfielder permanently, and they will have to pay a fee in the region of £10.5 million to do so.
In Germany, rivals Schalke and Bayer Leverkusen are ready to take a gamble on him. Everton and West Ham are lurking as well, and could move for him.
Kagawa is a good player, no doubt, but Everton probably do not need him. They are well stocked in their attacking department, and their priority lies elsewhere.
Nevertheless, Kagawa will bring with him loads of experience and quality, and it will be interesting to see whether Everton or West Ham make any concrete effort to sign him.