The defender is one of the players out of contract at the end of the season.
Since joining the club last summer he has been one of the most consistent performers and is highly regarded by supporters.
He showed his quality at both ends in the 2-0 win over St Mirren on Saturday, notching his fourth goal of the season with a fine free-kick.
“We’ve put an offer to him,” Neilson said. "Joe Savage is dealing with that and it’s coming back and forward as it always does.
"Hopefully we can get Stephen tied up because he has been one of our better players this season, and probably last season as well in terms of consistency.”
For many supporters of the Tynecastle club, Kingsley is one of the key names they want on a new deal.
Others in their final year include Craig Gordon, Craig Halkett, John Souttar and Peter Haring.
Neilson is keen to get “a number of them” tied up. The Hearts boss is more than happy playing those whose deal does expire.
“People always say going into the last year of their contract might affect them but in my experience it affects them for the good because they have to perform, whether it’s for a new contract here and for a contract somewhere else.
“So they have to perform.
“It’s the guys who sign the three, four and five year deals that you have to worry about because the tools can be downed and the cigar comes out sometimes.”