The club have opened talks with full-backs Michael Smith and Stephen Kingsley.
Neilson is keen to tie both down on extended deals with their contracts expiring at the end of the season.
Kingsley has been one of the signings of the season across the whole of Scottish football, Hearts picking up the Scotland international on a free after he left Hull City during the summer.
Neilson has heard positive messages from his left-back about staying beyond this campaign.
"We’re very hopeful, we’ve already spoken to him and he’s comfortable here,” he said.
“He’s moved back up the road, he’s got a kid now and got a house just outside Stirling and we’re very hopeful we’ll get something tied up and we’re in negotiations with him.”
‘Great place for him’
There was a degree of uncertainty amongst some fans due to Kingsley's injury record down in England, but the 26-year-old has arguably been the club's best player so far, playing 11 times.
Neilson said: “That was the major concern for both parties to be honest, we weren’t sure how he was going to be having been out for a long time and he admitted himself he wasn’t sure how he’d be and how his body would hold up to it.
"But we felt this was a great place for him, firstly we have brilliant facilities here and he’s back up the road, settled and has family around him. And also, with 27 games it’s not like the English Championship where you are playing Saturday-Tuesday, Saturday-Tuesday, you have time to play and recover.
“I think he has shown he has real quality. He’s just concentrating on playing week-in, week-out. It’s still early days but I’ve been pleased with everything he has shown so far.”
The new Takis?
On top of that, there is certainly an argument to be made he is the best left-back at Hearts since Takis Fyssas, although Lee Wallace would certainly have something to say about that.
Neilson also isn't ruling out further Scotland recognition, albeit with Andy Robertson and Kieran Tierney ahead of him.
“It’s been a problem position for us for god knows how many years,” he said.
“Taky was a top, top player, he won the European Championships but he has that calmness about him. It’s important, especially at Hearts, your defence has to be solid but also pretty calm.
"I think the best defenders at this club have been calm and been strong characters and I see that in Stephen.”
Neilson added: “I think he could potentially get into the international set-up. The issue is he has a couple of world class players ahead of him.”
‘Same kind of character’
While Kingsley is the new kid on the block, Smith is a Tynecastle stalwart and a hugely popular player with the fans since joining from Peterborough United in 2017.
He has made more than 110 appearances for the club and has become Mr Reliable, no matter which of the numerous positions he has been fielded in.
“We’ve already spoken to Michael’s agent as well,” Neilson said.
“Similar to Stephen, same kind of character. He is pretty level headed and we’ve been really pleased with him as well."