The Armenia international, who scored 25 goals in 28 top-flight appearances last season, has been heavily linked with a switch to the Reds in recent weeks.
On Thursday, the Shakhtar chief executive Sergei Palkin revealed Dortmund had failed in a £19.5m bid for the 24-year-old, with the Ukraine Premier League champions demanding a £23m fee.
And Palkin insisted Shakhtar are keen to retain the services of a key player in their side but would be willing to weigh up an offers from his potential suitors.
“Henrikh is an important player in our team. Shakhtar wants to keep him, but we are willing to listen and consider all suggestions for a transfer,” Palkin told Russian newspaper Izvestia.
“We have already parted with Willian [to Anzhi] and Fernandinho [to Manchester City], but the club will not just sell players.
“In the near future we will also gain quality, designed to replace the leading players, possibly including Henrikh.”
Shakhtar, who have won three straight top-flight titles, have already lost Willian to Anzhi Makhachkala, while Fernandinho completed a switch to Premier League outfit Manchester City earlier in June.