The player's representative Martin Schoots claimed that the 19-year-old had rejected the chance to join Roberto Mancini’s side.
"Manchester City strongly refute any suggestion that an offer has been made either to the player or his agent,” a club spokesman said.
Schoots had earlier told De Telegraaf: "Christian finds it a great honour that one of the biggest clubs in the world came to him and sees a big player in him.
"But his feeling says this is not the right time yet to make a transfer to Manchester. It's the feeling first and the money second."
Eriksen has made 43 senior appearances for Ajax since joining from Danish side OB in 2008.