The popular Austrian midfielder is out of contract at the end of the season and is the final of the club’s first-team stars to put pen to paper on a new deal.
Hearts have managed to tie down Craig Gordon, Craig Halkett, Stephen Kingsely, Andy Halliday and Barrie McKay on contract extensions.
Manager Robbie Neilson and sporting director Joe Savage are keen for Haring to join that list.
The player, who joined Hearts from SV Ried in 2018, was said to be considering his options.
Speaking ahead of the club's Scottish Cup final on Saturday, Haring gave an indication that his preference is to stay at Tynecastle Park, while he confirmed it wasn't a case of waiting until after the showcase occasion.
“Not really, we’re speaking with each other and trying to make it happen," he said. “Hopefully we can get there.”