Wigan Athletic have been told they will need to increase their bid if they want to land Callum Paterson.
Hearts head coach Robbie Neilson revealed they had rejected a second offer from Latics.
The 21-year-old is in demand but the capital club are willing to hold onto the defender, who has just 12 months remaining on his current deal.
Neilson said the Championship club’s valuation of Paterson fell “substantially” below the asking price.
He said: “There’s been another offer in from Wigan but we knocked it back. The two clubs are miles apart in the valuations of the player.
“We believe he is a real asset to us, he is a Scottish international, has played a lot of games for us and scored a lot of goals. He is back in the Scotland set-up for the next qualifying group.
“We value the player at a price and they have come in significantly below that. The valuation differences between the two clubs is vast and unless Wigan are prepared to move substantially, he will be here after the window.”