Ajax's director of football Marc Overmars has revealed they enquired about signing van Ginkel on loan as a possibile replacement for Tottenham target Christian Eriksen.
Van Ginkel only joined Chelsea from Vitesse Arnhem, but the 20-year-old has yet to start a game for Jose Mourinho's men so far this season.
Ajax were hoping to persuade Chelsea to allow them to take Dutch international van Ginkel on a season-long loan - but Chelsea have rejected their overtures, according to Overmars.
"We would like to see van Ginkel playing at Ajax," Overmars told NIS.
"For that type of player we are willing to pay top price.
"I've tried, but Chelsea will not let him go."
Overmars admits they are struggling to find a replacement for Eriksen should he seal his proposed move to Tottenham.
"It is also currently difficult for us," said Overmars when asked about replacing Eriksen.