The Foxes frontman will see his current deal expire next summer.
The 28-year-old has spent the last two-and-a-half years at the King Power Stadium, and has been a regular source of goals throughout that time.
He has no desire to try his luck anywhere else, after recently becoming a father for the first time, and would welcome the opportunity to sit down with the club and thrash out fresh terms.
Nugent told the Leicester Mercury: "We haven't sat down and talked yet, but I hope to soon.
"When Christmas comes, my agent and I will sit down and talk to the gaffer (Nigel Pearson) and Terry (Robinson, director of football) and try to do a deal.
"I really hope we can because I want to stay here. The lads are quality and the coaching staff are quality. I am really enjoying being at the club.
"This is my third year so, hopefully, I can stay for a few more years.
"I am still renting a place but if I sign a new contract then, with the baby now here, we will buy a place.
"Hopefully that can get sorted and I can be a Leicester player for a few years to come.
"I am concentrating on my Leicester career and I love it here so, hopefully, we can sort something out for next year."