Ajax say 17-year-olds John Goossens and Jeffrey Sarpong, who both impressed in the Under-17 World Championship in Peru, have been approached by Chelsea.
"What is happening here is really crazy," Ajax director Arie van Eijden told AD Sportwereld.
"We are thinking about what we can do to prevent this from happening. You would think that agents also think in the interest of clubs like Ajax."
Ajax claim Chelsea's technical director Frank Arnesen, a former player with the Dutch side, has contacted Soren Lerby, the agent of both players, to discuss a transfer with the duo, who have yet to sign professional contracts.
"It is impossible for us to give all juniors a contract already," van Eijden said.
According to Fifa rules, Chelsea can sign the players - Goossens is a forward and Sarpong a midfielder - for no more than £200,000 but Ajax are hoping the teenagers and their parents choose to sign a contract with them.
Chelsea have refused to comment on the story.