Peter Haring has been offered a new Hearts contract, according to a report.
And the Gorgie club remain in talks with Barrie McKay after he told MailSport he wanted to stay in Edinburgh long-term.
Austrian midfielder Haring has become a fans' favourite since signing in 2018, battling back from a pelvic injury that kept him out for over a year.
He is yet to ink a fresh set of terms at Tynecastle.
But Robbie Neilson has made his move to tie him down for longer, according to the Edinburgh Evening News, with negotiations ongoing with the former SV Ried man and also academy graduate Connor Smith, currently on loan at Queen's Park.
Injuries to Cammy Devlin and Beni Baningime - the latter out for up to nine months - have underlined the 28-year-old Haring's importance.
Winger McKay, meanwhile, said last week: "I’m not one of these people who thinks about leaving somewhere. I’m enjoying my football.
"It’s the first time in a long time I’ve been able to say it’s not a chore.
"We’ve been on such a high this season and it’s exciting to see how we can finish the campaign. I’d be open to staying longer at Hearts."