Sky Sources understand Hearts have rejected an improved offer from Wigan Athletic for right back Callum Paterson.
The Edinburgh club rejected an initial offer for the Scotland international from the Championship outfit last week.
Paterson's contract expires at the end of the season and can sign a pre-contract agreement in January.
The 21-year-old has become a vital cog in Robbie Neilson's set-up in recent seasons and has made nearly 150 appearances since emerging from the Riccarton youth academy four years ago. He has played in all eight of Hearts European and domestic fixtures this season.
Because of his age, Paterson will not leave Tynecastle for free at the end of his contract as any move would be subject to a compensation payment of around £300,000.