The 20-year-old midfielder completed a move from Vitesse believed to be worth in the region of €9.3 million on Thursday, but had also been the subject of interest from the Dutch champions.
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And Overmars, who starred in the Premier League for Arsenal during his playing days, believes his compatriot may have made the wrong choice.
"Van Ginkel is a great young talent and we would have liked him to come to Ajax," Overmars told BBC Sport.
"Whether it is too early for him to go to Chelsea or not, I don't know. With us, he would have played a lot of games and played in the Champions League.
"We couldn't have a discussion with the player as Chelsea have a co-operation agreement with Vitesse and were first choice. The important thing for the player is that he gets minutes in the first team. Hopefully the deal goes well and he will get into the team."
Despite his tender years, Van Ginkel already has one senior cap with the Netherlands national team to his name.
The midfielder made 41 appearances for Eredivisie outfit Vitesse last season, scoring 12 goals in the process.