The Amsterdam side refuse to meet Heerenveen's valuation for the player, although the Friezen feel a transfer is still an option
The Netherlands international is one of the Godenzonen's primary transfer targets ahead of the 2012-13 campaign, but they have failed to reach an agreement with the player's current club.
Heerenveen have reportedly set a €6 million asking price for Narsingh, while Ajax are not willing to pay in excess of €3m.
"The sky's no longer the limit at Ajax. If clubs set unrealistic asking prices for their players, we are pulling out," Overmars was quoted as saying by De Telegraaf.
"That's also the case when it comes to wages. Perhaps we can sign Luciano next year."
Meanwhile, Narsingh's agent has blamed Heerenveen for the winger's failed transfer to Amsterdam.
"It looks like they don't realise yet we're in an economical crisis. The only thing that can make this transfer go ahead is Heerenveen dropping their asking price, but I can't see that happen," Mino Raiola said.
Meanwhile, Heerenveen sporting director Johan Hansma revealed that the club will sell Narsingh to PSV if Ajax don't increase their offer.
"Ajax are still more than welcome, but PSV have offered more than them. We'll have to discuss this. There are all kinds of constructions possible, though," he said.
The 21-year-old Narsingh's current deal runs until the summer of 2013. Aside from Ajax and PSV, Fulham are also closely monitoring his situation at Heerenveen.
Meanwhile, Voetbal International claims that PSV have increased their initial offer for Narsingh and that the Eindhoven-based club are leading the race for the 21-year-old starlet.