The 19-year-old Croatia international has been linked with a move away from his present side, with Manchester United and Arsenal seen among possible destinations.
But Kovacic, who moved to the Italian giants from Dinamo Zagreb in 2013, insists he is enjoying his football and wants to stay and improve.
He told Sportske Novosti: "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 better player, how to help my team to get much better results.
"I'm young, so I have a lot of 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."