The Armenia international has shone domestically and in Europe this season, allowing him to catch the eye of clubs outside of the Ukraine.
Premier League heavyweights such as Manchester City and Chelsea are said to be among his suitors, along with Primera Liga giants Barcelona.
Mkhitaryan has had his head turned by the speculation, with there a desire on his part to test himself at the highest level.
The 24-year-old is under contract at Shakhtar until 2015, but admits he is prepared to force through a transfer if attractive offers are put to him.
He said: "For every player to play for the strongest clubs in the world is a dream, and I will do everything possible to move this summer to a different team."