The Seagulls were close to sealing a deal for the 23-year-old earlier this month but the move broke down after Albion were unable to finalise personal terms.
The Ghana international now looks set to complete a move to West Ham, despite reported interest from Arsenal.
Kudus bagged his first hat-trick for Ajax in Thursday night’s 4-1 UEFA Europa League play-off first leg victory at perennial Bulgarian champions Ludogorets Razgrad.
And, speaking to Dutch television channel RTL 7 after the match, Kudus admitted he may have played his last game for Ajax.
The Ghanaian remained coy about rumours linking him to West Ham but admitted the Irons were a ‘good club’.
But, in a separate post-match interview with Dutch outlet AD Sportwereld, Kudus made it clear he would almost certainly be joining the Hammers.
He said “I spoke with West Ham United. I am now waiting for an agreement between the clubs.
“I think every player dreams of playing in the Premier League. So when the opportunity comes, why not?
“I started my fourth season at Ajax and I feel ready for the next challenge.”
Kudus joined Ajax from Danish side FC Nordsjælland in 2020 and has gone on to make 87 appearances for the four-time European Cup winners, scoring 27 goals.