The 18-year-old has impressed for the Amsterdam side since since returning from a brief spell out of the starting XI this season, scoring six goals and setting up four in the Eredivisie.
Manchester United have been reported to have an interest in the winger and although he aims to stay in his homeland for a while, he admits he would consider a move to some of the top sides in England.
"If you get a nice offer, you never know," he told Helden .
And Kluivert, son of legendary Barcelona striker Patrick, is also not ruling out a move to Spain. He added: "Everywhere I go abroad they know my father, he often asked: 'Come to Barcelona, I'll give a tour of Camp Nou'.
"I really wanted to go to Barcelona instead of Real Madrid. Barcelona is in my heart, but who am I to say no to Real Madrid?"
Kluivert's contract expires in June 2019 and talks have begun over a new deal with the capital club, but director of football Overmars says they have had to deal with approaches for him and a few of his highly-rated team-mates.
"I am discussing his contract with his agent Mino Raiola and I still have good hope that we will reach an agreement," Overmars told De Telegraaf .
"There is a lot of interest for a lot of the boys. Clubs have reported for Hakim Ziyech, Andre Onana, Matthijs de Ligt, David Neres and Justin Kluivert.
"Last year we showed what we can do in the Europa League, we'd prefer to experience another season like that and if we keep our current selection together, there is a good basis."