The Croatia international completed a season-long loan move to the west London side from the Champions League holders in the 2018 summer transfer window.
Kovacic struggled to hold down a regular starting spot during his three seasons at Real Madrid to raise questions about his long-term future at The Bernbeu.
The 24-year-old saw his stock rise in the summer after Kovavic helped Croatia to reach the World Cup final after a dramatic 2-1 win over England in the semi-finals.
Croatia lost 4-2 to France in the final but Kovavic’s performances in Russia earned the versatile midfielder a switch to Chelsea FC in the 2018 summer transfer window.
Maurizio Sarri has started the on-loan midfielder six times in the Premier League this season, while the World Cup finalist has made a further two appearances from the bench.
Asked about a permanent switch to Chelsea FC following his impressive start to life at Stamford Bridge, Kovacic is quoted as saying by the Evening Standard:
“It’s too early for these questions, I am here and very happy.
“[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.”
Kovacic produced an assist for Eden Hazard in Chelsea FC’s 1-1 draw with Liverpool FC in the Premier League at Stamford Bridge at the end of September.
The Croatian star is competing with N’Golo Kante and Jorginho for a starting spot in the middle of the park in the Chelsea FC team this season.
Kovacic won the La Liga title and three Champions League crowns during his 36 months at the Spanish giants following his move from Inter Milan in 2015.
Chelsea FC will take on Derby County in the Carabao Cup on Wednesday night before the west London side welcome Crystal Palace to Stamford Bridge in the Premier League on Sunday.
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