Palkin on Wednesday claimed Champions League runners-up Borussia Dortmund had failed with a bid of £19.5million, suggesting £25million was nearer the mark.
Liverpool are interested in the Armenia international but any deal for a player who set a Ukrainian league scoring record with 25 goals last season is a complicated one.
Russian big spenders Anzhi Makhachkala are now also reported to have entered the race.
"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."