Hearts technical director Steven Naismith is keen to bring Peterborough defender Frankie Kent to Tynecastle.
The centre back still has one year remaining on his deal at Posh but it is thought that manager Darren Ferguson would listen to offers for the 27-year-old.
The Gorgie side are keen to bolster their defence with Craig Halkett still working his way back from a cruciate ligament injury.
Kent came through the Arsenal academy before joining Colchester in 2012.
After seven years with the U’s, he made the move to London Road in summer 2019 and has gone on to make nearly 150 league appearances for Peterborough.
That includes a total of 49 outings in all competition last season as Ferguson’s team were beaten in a dramatic League One play-off semi-final by Sheffield Wednesday.
Goalkeeper Michael McGovern remains Hearts’ only summer recruit to date with just a fortnight until the new Premiership campaign begins.
Hearts have also agreed terms with Western Sydney Wanderers midfielder Calem Nieuwenhof but the Australian is still to be granted a work permit.