Republic of Ireland Under-21 international Judge is set to return to the Premier League club in January when his loan spell with the Magpies ends.
Former Rovers boss Ince wants to sign Judge on a permanent deal, but admits he is unsure whether they will now be willing to sell.
"Things have changed with Sam being sacked so I'm not sure what his situation is, but I would love to keep him," Ince told the Nottingham Post.
"I had him at Blackburn before I came here and he is a talented lad and an infectious character. I'm trying to sit down with his agent to get a deal done on a long-term basis.
"He will go back to Blackburn in January but we will hope to bring him back straight away on a long-term contract."