Both Arsenal and Manchester United are understood to be monitoring the 19-year-old Croatian international.
However, Kovacic is eager to remain at the San Siro for the remainder of his four-year contract.
"The press have to write something," he told Sportske Novosti. "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."
Kovacic joined Inter from Dinamo Zagreb in January 2013.