As reported by Sky Sports, the teenage Inter Milan star insists he is happy at the San Siro and has no intention of leaving the club - even for somewhere like United or Arsenal.
The two Premier League sides have been linked with the 19-year-old attacking midfielder in the recent past, with United boss David Moyes thought to be weighing up a swap deal involving Javier Hernandez at that one stage.
But Kovacic insists he wants to stay in Milan with Inter for the time being.
Speaking to Sportske Novosti, he said: "The press have to write something. I may be young but I have learned so far that journalists must speculate on something every day.
"But all that is not a burden for me. I have a contract until 2017 and my future is with Inter. I'm really happy that I'm part of such a great club.
"So all I'm thinking right now is how to become a better player, how to help my team to get much better results. I'm young, so I have a lot time. And I'm still adapting.
"But I'm happy and also everybody at Inter are happy with me. And that counts the most to me."
Kovacic was linked with a Premier League move - specifically Manchester United - before he signed for Inter Milan from Dinamo Zagreb in the winter transfer window of 2013.
The deal, reportedly worth €15m, saw Kovacic take the number 10 shirt previously occupied by Wesley Sneijder. Since his debut in February last year, the Croatian teen has made 40 league appearances for Inter Milan, with his performances good enough to attract intention from Arsenal among others.