Eto'o, 33, is a free agent after netting 12 goals for Chelsea last season.
"Samuel seemed very hungry to play for Ajax. He is fit and has a great drive to succeed once again," Overmars told Voetbal International.
"We don't want to block the growing process of our talents like [Arkadiusz] Milik and [Richairo] Zivkovic, but if it is possible to sign a world class player like Eto'o, then why not? It will be fantastic."
Eto'o, a record four-time African Footballer of the Year, is also believed to be on Sunderland's radar having rejected a move to West Ham in the off-season.