The two clubs had agreed a transfer fee for the Dutch international, while the 24-year-old was also believed to have accepted personal terms over a switch to the Mestalla.
However, reports have now suggested that the La Liga outfit are ready to end their interest in the full-back.
"It may be that my transfer to Valencia is off. If no big club comes in for me, I will stay at Ajax," Van der Wiel told AD Sportwereld.
Liverpool and Chelsea have both been credited with an interest in the defender's services.