The Red Devils have been linked with a swoop for the 17-year-old but Zagreb insist they have had no contact from the club about a possible deal.
"You should ask them, if they are interested in Kovacic," Mamic told the PA. "We didn't have any contact with Manchester or Sir Alex Ferguson or talks on that subject, nor have we received any kind of offer from them."
Goal.com revealed that Sir Alex has scouted the player personally, and while no offer has been made, the reigning Premier League champions are leading the race to sign the player regarded as the 'next Luka Modric'.
Arsenal, Juventus and Bayern Munich are also believed to be interested in signing the talented midfielder, but the Gunners backed out on a move feeling Zagreb's valuation was too high.
However, Mamic revealed other top clubs from around Europe have taken an interest in Kovacic so United may face competition for his signature.
He added: "We cannot hide the fact that that many clubs are following Mateo Kovacic.
"Scouts from the biggest European clubs are coming to our games and analysing his capabilities. There is no point in naming them, as they are really the top European clubs."