The Cameroon international - who is yet to make an appearance this season as he serves a doping suspension - is due to become a free agent in the summer of 2022.
Ajax have previously attempted to tie Onana down to a new deal, but Overmars has now conceded that the shot-stopper will be seeking pastures new in the near future.
Speaking to Ziggo Sport, the ex-Arsenal attacker said: "We are not currently working on contract extension, no. We tried, but it didn't work.
"You make choices and then it has to come from both sides. We didn't feel like he really wanted to. I read somewhere that we pulled the plug and that's right. We do that for a reason.
"At a certain point you also get to the point that it has to yield a decent amount. If the amount is not enough, then in July for nothing."
Onana has been tipped to head to Arsenal as a possible replacement for Bernd Leno, although Inter Milan are rumoured to be at the head of the queue as they eye Samir Handanovic's successor. body check tags ::