Hudson-Odoi played a significant role in helping Forest secure a spot in European competition for the first time in 30 years during the 2024-25 season.
He made 36 appearances across all competitions and contributed five goals and three assists.
According to a source, talks with Hudson-Odoi are ongoing, and Forest has presented him with a new deal.
There is also interest from clubs abroad, including Napoli, but it is still an early stage in the negotiations.
Hudson-Odoi was reportedly happy with his season, but a hamstring injury at the end was disappointing.