City boss Roberto Mancini reportedly watched the 24-year-old in action for Ajax against Twente on Sunday.
De Boer told De Telegraaf: “[Assistant coach] Danny Blind told me that Mancini was at the stadium and I know that Manchester City are interested in signing him. One and one is two.”
Vertonghen has also been linked with the likes of Arsenal and Manchester United.
Vertonghen’s current contract at Ajax is set to expire in the summer of 2013.