The Scotland international has turned himself into an important member of Darren Moore’s side, starting in five of the last eight matches they have played.
His contract at Hillsborough has entered the final five months though, with his boyhood club showing interest in taking him back to Edinburgh.
They have already made two attempts to sign Paterson, both of which have already been rejected by Moore’s outfit.
Sheffield Wednesday, a side currently placed second in the League One table and fighting for automatic promotion, do not want to part ways with a player who they feel could be crucial in their attempt.
Hearts though have no desire to give up and could come up with a pre-contract agreement to sign Paterson when his current deal with the Owls ends in the summer.
Hearts are open to the idea of offering the striker a long-term deal if he decides to sign for them.
Sheffield Wednesday are also taking into consideration the fact that if they decide to sell Paterson now they might not get in a replacement in time before the transfer window shuts on Tuesday.
