Jose Mourinho looks set to make the youngster his first Chelsea signing since returning to Stamford Bridge as the Blues are keen to add some fresh blood to their midfield.
Ajax were eager to sign Van Ginkel, too, but sporting director Marc Overmars admitted earlier this week that his club cannot compete with Chelsea in securing the midfielder's signature. The 20-year-old, however, has remained coy on his future for now.
"The Premier League is a very good league, I think every young player wants to play there," he told Sky Sports News Radio.
"I know what people want to hear, but I'm not going to say anything about that now.
"I have to focus on this tournament. After that, I will think about my future - not now."
Van Ginkel was named the Netherlands' Talent of the Year in 2012-13 and scored eight times in 33 Eredivisie games for Vitesse, helping them to fourth place in the table.
His current contract with the Arnhem side runs until the summer of 2015, but they are ready to cash in on Van Ginkel for a fee of €8-10 million.