De Jong has been watched personally by Toon boss Alan Pardew in recent weeks.
Kluivert, McClaren's No.2 at FC Twente, said: "Luuk [de Jong] is going to be the No.1 striker for Holland in the very near future.
"He has everything a striker needs.
"Here at FC Twente we are grooming him for a future with one of Europe's biggest clubs.
"He can become a European giant.''