Mkhitaryan is the Reds' top transfer target summer, but it appeared a move to Anfield was in doubt after the 24-year-old denied speculation linking him with Liverpool.
Liverpool manager Brendan Rodgers has reportedly sanctioned a £20million-plus bid for the Armenian international, and while Mkhitaryan has been warned by Shakhtar that he must report for pre-season training - they have now accepted he could be sold.
"Henrikh is an important player in our team," chief executive Sergei Palkin told Russian newspaper Izvestia. "Shakhtar want to keep him, but we are willing to listen and consider all suggestions for a transfer.