Midfielder De Jong, 21, and teenage defender De Ligt are the most coveted youngsters emerging from Ajax's latest crop of talented prospects.
Werder Bremen's Klaassen played alongside the pair in Amsterdam and expects them to realise their potential.
"In a couple of years you will see a lot of [Ajax] players at good teams," Klaassen told Omnisport.
"For example, De Jong and De Ligt. I think they are amazing.
"De Ligt at 17 was playing like he was 30 years old because he was so massive and so good. I think they will have great careers."
La Liga champions Barca are believed to have stepped up their interest in De Jong following Andres Iniesta's departure earlier this year.
While Klaassen is wary of anointing him as the heir to the Spain great, he can envisage his compatriot becoming a hit at Camp Nou.
"It's always hard to compare to players like Iniesta for example, because he's one of the best midfield players ever," the ex-Everton man said.
"But I think Frenkie is really good and maybe he can make the step to Barcelona and do well, so why not?"