The Dutch giants had lined up Van Ginkel as a replacement for Tottenham-bound Christian Eriksen, with the Danish international on the verge of completing a £10 million move to White Hart Lane.
But Ajax have been stopped in their tracks having been told that Van Ginkel is not available, despite Jose Mourinho only using the 20-year-old playmaker sporadically so far this season.
With World Cup 2014 just around the corner, Van Ginkel is keen to be playing regular first-team football in an attempt to book his place in Holland's 23-man squad next summer.
The Dutch international's representatives are already concerned by Van Ginkel's lack of involvement at Stamford Bridge, with the former Vitesse Arnhem star left out of the squad altogether for the goalless draw with Manchester United on Monday.
Chelsea officials had allayed Van Ginkel's fears over playing time prior to completing his signing, but the uncertainty surrounding the player's situation was hoping to be capitalised on by Ajax, though their offer has been rebuffed.