West Ham are keen on Manchester United pair Harry Maguire and Scott McTominay, while Gianluca Scamacca has left the club to join Atalanta.
West Ham are yet to make a signing this summer despite selling Declan Rice to Arsenal in a deal that could end up being worth £105m.
They are in advanced talks with Ajax over Mexico midfielder Edson Alvarez.
But after Saturday's 4-0 defeat by Bayer Leverkusen, there is greater momentum behind their recruitment drive.
Whether West Ham can reach either the fee or salary to conclude a deal is open to question.