The likes of Callum Paterson, Jason Holt and Dylan McGowan have featured heavily in the first team in recent months after the club cut their wage budget in the summer.
And McGlynn revealed they were on the brink of agreeing new deals with some players.
McGlynn, who has seen the club sell David Templeton and Ryan McGowan this season in a bid to stem a cash flow crisis, told Hearts TV: "I'm hoping we are going to have news for the fans shortly, and give them some good news.
"We are working with a number of players at the minute and we would like to give some good news for the fans.
"It's been a difficult season and a lot of doom and gloom but I can rest assured the best young players will be plying their trade at Tynecastle next season."
Meanwhile, right-back Jamie Hamill is still to return to full training after being troubled by knee pain in his comeback from a cruciate ligament injury.
McGlynn revealed earlier this month that Hamill had suffered a setback in his bid to return from the injury he suffered in April.
McGlynn, who is without suspended pair Marius Zaliukas and Ryan Stevenson for Saturday's Clydesdale Bank Premier League clash at Celtic Park, said: "He's now trying to get back into working in the rehab room with Rob Marshall, the physio.
"We just have to see how he gets along, if he can progress and get back into running and get back to training with the first team.
Hopefully that's not too far away."