The 19-year-old claimed he turned down a move to Napoli in January to focus on his development in Holland, before admitting his interest in a "dream" move to Barca within three years.
And De Boer believes the Spanish giants will be prove too great an opportunity to turn down.
"You can always say no, but that will be difficult," he told Fox Sports when asked about the possible interest of Barcelona.
Bazoer has also been linked with a host of Premier League sides, including Chelsea.
READ MORE | The Ajax wonderkid dreaming of Barca
Yet De Boer warned against a move to the Blues, citing the frustrations of Marco van Ginkel, who who joined from Vitesse in 2013 but has been shipped out on loan to AC Milan, Stoke City and PSV.
He said: "He told that he is only focusing on Ajax and the matches that are about to come.
"On that point he takes big steps. Earlier he was able to be busy with side issues, but not anymore.
"It's all about the perspective at another club.
"If you have the idea that you are going to play weekly, than I would take the step. But if you have the idea to arrive in a Marco van Ginkel scenario, than I would stay where I am."