Jim Jefferies has urged Hearts to hold on to left-back Lee Wallace this summer if there is no sizeable offer - even if it means him leaving for nothing.
But the Hearts manager is hopeful the Scotland international will extend his contract, which expires next summer, despite Rangers failing with two bids.
"If the offer is low, we're better off keeping him," said Jefferies.
"As he would be worth more to us in the short time he'd be here. Lee is a great asset to the club."
Hearts have announced that they had begun talks about extending 23-year-old Wallace's contract after rejecting an offer of around £1m from Rangers.
"The problem is that he's in the last year of his contract," said Jefferies.
"It's the same with any player at any club - it makes things a bit more difficult.
"If we can get him on a long-term contract then his price will go up.
"The club will try to extend his contract. But, if he wants to move on, clubs will be in for him."
Even so, Jefferies stressed that the interest from Ibrox would not effect the defender.
"He has a great attitude," said the manager. "I've seen players that let speculation effect them and they're at your door every day asking what's happening.
"We've never had a problem with Lee.
"He's been here a long time. If he does move on, he would like the club to get decent money for him."
Wallace has had an injury problem during pre-season but is expected to be fit to play for Hearts this weekend in one of two friendly matches against either Livingston on Saturday or Royal Anterp on Sunday.
Meanwhile, Jefferies said that Kevin Kyle is ahead of schedule in his potential return to first-team action and that the striker will be ready to resume training in three to four weeks after initially ruling him out until the end of the year.
Winger Andrew Driver has resumed full training with the first-team squad, but Jefferies says it will be a couple of weeks before he is ready to compete in matches.