The Dutch giants had also set their sights on the promising midfielder, but he is destined to make the move to the Europa League winners instead
Sporting director Marc Overmars has admitted that the Eredivisie champions cannot compete financially with Chelsea.
The Amsterdam giants were keen to sign the Netherlands international ahead of the 2013-14 campaign, but Van Ginkel will make the move to Chelsea instead this summer as he is set to become Jose Mourinho's first signing since his return to Stamford Bridge, much to the disappointment of Ajax.
"Ajax were very interested in Van Ginkel and we were willing to go quite far," Overmars was quoted as saying by Voetbal International.
"But if we have to compete with one of the big clubs from England it is always going to be difficult for us. We cannot beat Chelsea's financial resources."
Van Ginkel has a contract with Vitesse until the summer of 2015, but the Arnhem side are ready to cash in on the 20-year-old for a fee in the region of €8-10 million.
The midfielder has been one of the stars of the Under-21 European championship in Israel this summer as Netherlands have qualified for the semi-finals after wins over Germany and Russia.