The English Championship club, managed by former Scotland defender Gary Caldwell, are keen to take Paterson to England but have been rebuffed in their first attempt.
They will return with a second offer, although it remains to be seen by how much they will increase their initial six-figure proposal.
Tynecastle officials mulled over Wigan’s interest but decided the bid did not meet their valuation of the 21-year-old Scotland internationalist.
Paterson is in the final year of his contract and is unlikely to sign an extension. Hearts want to keep him beyond the end of the summer transfer window but Wigan and other English clubs are interested in taking him south.
Neilson recently spoke about his desire to keep Paterson at Tynecastle, insisting that he would not be sold on the cheap.