In a statement, Parry insisted George Gillett and Tom Hicks are still backing Liverpool boss Rafa Benitez.
"There has been a lot of comment regarding our position with regards to Gareth Barry," Parry said on Liverpool's official website.
"This is not about questioning the manager's judgment or the ability of a particular player. The owners have clearly demonstrated throughout the year they are willing to back Rafa in the transfer market and will continue to do so.
"It is obviously the selling club's prerogative to put whatever price they want on the player, but on this occasion Liverpool think the price quoted is too high."