Tottenham Hotspur are said to be focusing their attention on players from four European clubs.
Tottenham were linked with a move for Van de Beek, who plays as a defensive midfielder for Ajax, earlier this week.
But they are also being credited with interest in the 20-year-old's clubmate Kluivert, along with Bayer Leverkusen attacking midfielder Kai Havertz.
Winger Kluivert, who is the son of Dutch legend Patrick, has played 31 times for the club at which his father made his name, scoring two goals and creating another six.
It is claimed that Ajax, from whom Tottenham signed defender Davinson Sanchez in August, are one of several European clubs on whom Mauricio Pochettino's scouting team are focusing, along with Leverkusen, Hoffenheim and Monaco.
Spurs have previously recruited Jan Vertonghen and Christian Eriksen from Ajax, as well as Son Heung-min from Leverkusen.
Havertz, 18, has played 36 times for the German side, scoring four goals and assisting another nine.