Maddison is reported to be valued at £20 million by the Canaries, amid interest from Premier League clubs such as West Ham, Leicester and Everton.
However, according to the 'Sun', Southampton seem to be the closest to matching this valuation for the player, who is recovering from a knee ligament injury sufferered on the last day of the season.
The 21 year-old scored 15 times for Norwich last campaign, and is a highly-rated prospect as his price tag suggests.