With his contract due to expire at the end of the season, the 25-year-old Scotland centre-back is free to talk to other clubs about a pre-contract from the start of December.
Neilson confirmed that Hearts have made Souttar a “really good offer”, but there is some doubt that they will be able to match what is could be on the table from clubs south of the border in the weeks ahead.
The Hearts head coach is well aware of the possibility that some clubs may put in a cut-price offer in a bid to sign his prize asset on the cheap when the January transfer window opens, but insists he would rather hold on to the defender until the end of the season than cash in early with a low offer.
"From our perspective, he's here until the end of the season unless we get a bid that we can't refuse,” Neilson said.
"Hopefully within that time we can negotiate a new contract. The owner and Joe Savage have been speaking to him and we've made him a really good offer, so it's just a case of trying to negotiate that.
"He's still a Hearts player and we've had good negotiations with him. We'll try as hard as we can to get him to stay.
"If he does decide it's time to move on, it will take a huge bid in January for that to happen, or he'll see out his contract and hopefully leave happy.
"He is a key player who will hopefully help us finish as high up the league as we can and go as far as we can in the cup, so you have to balance off the two sides of it and say 'what is keeping him (until the end of the season) worth?' and 'what is a transfer worth?'
"From my perspective as a coach, I'll be pushing to keep him here for as long as I can because he's such a key part of the team."