He may be only 24, but reports have claimed that his Ukrainian employers will demand around £25m for their Armenian international.
So, what would either club be getting for such a big outlay? Well, despite not being considered a striker, he was still able to score 25 goals in 28 outings in the Ukrainian top flight last season. What's more, he made 10 assists.
He also showed that he can cope with the demands of Champions League football, scoring on two occasions before Shakhtar were knocked out by eventual finalists Borussia Dortmund in the second round.
Below is a video compilation of some of Mkhitaryan's best moments for Shakhtar.