Van Ginkel is currently playing a starring role for Holland at the European Under-21 Championship and he is now said to be high on the Premier League club's wanted list.
Dutch giants Ajax are also keen, but Chelsea are in pole position given their close relationship with Vitesse, who they have an affiliation with.
Van Ginkel's agent Karel Jansen told De Telegraaf: "Chelsea are interested, we don't deny it.
"But there are more clubs. Ajax had made official contact with Vitesse, but they don't want to talk with them.
"The situation is that we wait until after the the European Championship and then will look for the best step.
"Marco still has two years under contract at the GelreDome, so we don't know if he will leave Arnhem but there isn't an agreement right now."
Chelsea's relationship with Vitesse is so close that the English club are reported to be helping them with the appointment of a new coach.