The Canaries are looking to bolster their squad following Gabriel Sara's departure to Galatasaray.
New Norwich head coach Johannes Hoff Thorup, familiar with young Ghanaian talent from his time at Nordsjaelland, is keen on Amankwah.
The 21-year-old joined Salzburg in 2021 and has since gained experience through loan spells at Liefering and Rheindorf Altach.
Last season marked a breakthrough for Amankwah, who made 27 appearances for Salzburg across all competitions, including his Champions League debut.
He made his debut for Ghana’s national team in March playing a total of 88 minutes in the friendlies against Nigeria and Uganda.
His performances have attracted interest from several clubs this summer, including Anderlecht, Sturm Graz, Nordsjaelland, Freiburg, Augsburg, and Stuttgart.
Norwich offered a clear path to first-team football and the allure of playing in England appealed to Amankwah.
The Canaries, who finished 6th in the Championship last season and reached the playoff semi-finals, are aiming for a return to the Premier League after their relegation in 2022.
Amankwah's signing could be a key step in achieving that goal.
