With first-team members like Christophe Berra, Aidy White and Elliott Frear in the final few weeks of their current agreements, the prospect of new deals has yet to be discussed.
Goalkeepers Zdenek Zlamal and Colin Doyle are also out of contract this summer but both are expected to move on. Doyle is on loan at Kilmarnock until the end of the campaign.
Talks are still ongoing regarding a new deal for midfielder Andy Irving and there have been discussions about signing on-loan Preston North End winger Josh Ginnelly permanently.
Former Hibs star Leigh Griffiths finally finds new club as striker set for foreign adventure
Edinburgh's Tynecastle Stadium: Here are 20 pictures from the 1950s and 1960s showing how much the Hearts ground has changed
Hearts confirm proposed kick-off times and alternative venue for Europa League play-offs
Lawrence Shankland reflects on partnership with Barrie McKay, missed chances and Martin Boyle stealing his thunder
Martin Boyle aims to see out rest of his career at Easter Road after stunning Hibs return
Manager Robbie Neilson told the Evening News that no more contract talks will start until Hearts know which league they will play in next season.
“We have to make sure we win the league first before we even think about any of that stuff,” said Neilson, whose team sit 12 points clear at the top of the Championship heading into Saturday’s match with Dundee at Tynecastle Park.
“I think it's important that we concentrate on getting over the line – and over the line by winning games – then when the conversation comes we can speak about it. At this moment in time, we are concentrating on the matches.”
Hearts hope to have full-back Michael Smith available to face Dundee after a calf-related problem forced him off against Inverness Caledonian Thistle last week.
Captain Steven Naismith remains touch and go after being substituted in the same game with a similar injury.