The reports, carried by the Daily Mirror, claim the Armenian international has caught the eye of Brendan Rodgers, and the Liverpool boss is reportedly monitoring his progress in Ukraine.
And the Shakhtar star has conceded he'll be looking to move on at the end of the season.
He said: "For every player, to play for the strongest clubs in the world is a dream, and the main goal. I will do everything possible to move this summer to a different team."
The Daily Mirror report claims any deal for the Armenian midfielder would likely be for a fee around the £25m mark.
But Shakhtar's elimination from the Champions League last-16 stage could smooth his exit from Ukraine this summer.
Liverpool have reportedly made him their "top target", but with Chelsea and Manchester City sniffing around, they could find it difficult to land their man.
Rodgers' team currently looks like it won't qualify for the Champions League next season, while Chelsea and City will probably be able to offer Mkhitaryan European football despite disappointing Premier League campaigns so far.