The Armenian international has been consistently linked with a move to Liverpool in recent weeks, with Reds boss Brendan Rodgers desperate to land a player he has identified as his top transfer target.
Borussia Dortmund are also believed to be monitoring Mkhitaryan's situation closely, with competition high to land the man who scored 25 league goals from midfield at Shakhtar last season.
Spurs believe that Mkhitaryan is still very much available and held preliminary talks with the player's representatives earlier this week in London, according to the Daily Mail.
Senior figures at White Hart Lane are currently trying to close a deal for Brazilian international Paulinho, but will reportedly turn their attention to securing Mkhitaryan's signature early next week.
Shakhtar are demanding a transfer fee of around £25m for their top scorer and have not given up hope of persuading the playmaker to stay next season.