The Dutch champions had set a deadline for the player to decide whether he wished to move to Amsterdam, but the Cameroonian refused to be pressured into making up his mind over his next move.
"Of course, Eto'o has the right to think about his future as long as he wants," Overmars told Voetbal International.
"But we're not going to wait for him anymore. We told him that we're not interested in any further talks."
Eto'o has been without a club since parting company with Chelsea at the end of the season and has since been linked with a host of European clubs, including Liverpool and former club Inter.