The 22-year-old is on loan at Meadow Lane from Blackburn until January and is out of contract at Ewood Park in the summer.
Judge has impressed in seven league appearances for the Magpies this season and fits Ince's vision of building a squad of promising young players capable of ultimately leading the club into the Championship.
Asked if he wants to sign Judge on a permanent deal, Ince said: "Yes. The idea is not just to bring in players on loan deals. We've got to bring in players on two or three-year contracts and say `this is my team`.
"I expect to be in the Championship. If we are not in the Championship in three-and-half years, I haven't done my job and I deserve to go."
Ince added: "Judge is a fantastic player. He has trained with some top players at Blackburn for most of his career, so we are looking to sit down with his people to sort something out."