Hearts insist Andy Driver will only leave for big money.
The Edinburgh club say they are willing to listen to offers for the winger, who has been linked with Chelsea, West Ham United, Wigan Athletic, Burnley and FC Twente.
But Jambos bosses want a "sizeable" transfer fee to be agreed before they will sanction any move for the 22-year-old, who is under contract until 2013.
Hearts director Sergejus Fedotovas told Hearts.TV: "We absolutely know what we want to achieve.
"We have had a number of discussions with a few clubs and I'm glad we have been getting very healthy interest in the player.
"If we get a proposal which falls within our expectations then we will consider it very seriously.
"If not, then we will keep the player for the benefit of the team."