The 24-year-old attacking midfielder revealed his desire to move to one of the "strongest clubs in the world" after impressing on the European stage with his current team
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And the Armenian has now indicated he is ready to take the next step in his career, with a number of top teams interested in a move, suggesting he will force a transfer should his employers not want to sell.
"For every player, to play for the strongest clubs in the world is a dream, and the main goal," the attacker was quoted as saying by the Mirror.
"I will do everything possible to move this summer to a different team."
Mkhitaryan helped Shakhtar progress from Group E of this season's Champions League ahead of the Blues, who are reportedly chasing his signature.
The west Londoners are expected to be busy in the summer, with interim boss Rafa Benitez already confirming his departure, while Frank Lampard's contract expires at the end of the season.