Subject to the deal being finalized, the fee is in the region of €40million. That would make it a club-record purchase, surpassing the price paid for Joao Pedro this summer, which was just under £30 million.
Ghana international Kudus is close to agreeing personal terms with the Premier League club.
The move has been driven by Brighton head coach Roberto De Zerbi, who views Kudus as a key target.
However, fellow Premier League side, Chelsea made contact with Ajax to express an interest in Kudus last weekend.
Kudus is under contract at Ajax until 2025 but rejected a one-year extension in April and is keen to leave the Johan Cruyff Arena.
He has spent three seasons in Amsterdam following his move from Danish side, FC Nordsjaelland.
The 22-year-old has scored 16 goals in 63 Eredivisie matches. He has scored seven goals in 24 appearances for Ghana, including two at the 2022 World Cup in the 3-2 group-stage win over South Korea.
Kudus has played as many as seven positions since his debut in Dutch football, operating all the way from a deep-lying No 6 to an out-and-out center-forward, with the majority of his time spent out on the right-wing running at the full-back.
WATCH Our latest Episode with Kennedy Agyapong in South Africa below:
Source: footballghana.com