The 21-year-old is considered one of the brightest prospects in the English second division following an incredible season that saw him score 15 goals and assist 11 more in 49 games in all competitions.
According to 'Sky Sports', both Southampton and Leicester have now seen bids worth an initial £22m plus £2m more in add-ons accepted by the 'Canaries' as they look to cut costs following the end of their parachute payments.
Other reports suggest that the deal will also include a 10% sell-on clause, though it will smash the record transfer fee paid for a Championship player regardless.
Maddison is currently recovering from a knee ligament injury suffered on the final day of the season, but is expected to be back in full training next month.
The England U21 international has attracted interest from a host of sides over the course of the last 12 months, with the likes of Manchester City, Tottenham and Liverpool all thought to have run the rule over the former Coventry man.
However, it appears that he is destined for either Leicester or Southampton, with Maddison set to decide on his new club in the coming days.