The Croatian midfielder is on a season-long loan at the London club from Real Madrid, and so far this season he has thrived under Maurizio Sarri.
However, when asked by the 'Evening Standard' about whether he might be interested in a permanent move, Kovacic was unwilling to elaborate.
"It’s too early for these questions, I am here and very happy," he said.
"[Playing regularly] is good, I’m a little bit tired. I was not used to playing every three or four games and here it is very tough football.
"You can’t relax against anybody so it’s a little bit difficult but I really enjoy it. We have a great team, great fans and the city is nice. I like it a lot here.
"I go around and I enjoy the city — it’s huge and I haven’t seen enough of it yet. I’m looking forward to getting to know it more. I’m enjoying it. What’s the most interesting thing I’ve seen so far? The stadium.
"I don’t do anything special. I spend a lot of time in Cobham because I need to prepare myself for training and every game but after that I go home and enjoy time with my wife.
"Nothing special, we go for dinner, we live in the city so we are walking a lot. My family enjoys the city and that’s the most important thing for me in the end."