Hearts insist Andy Driver will only leave for big money.
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."