The Blues boss also signalled his intent to keep hold of Gonzalo Higuain, but the club's ability to do so might be affected by the transfer ban hanging over them.
Chelsea have a hearing with Fifa's Appeals Committee over the status of a suspension of the ban, at least temporarily, with the governing body turning down the club's initial appeal.
There still isn't clarity on how Chelsea's summer might pan out as the club's legal battle with the Court Arbitration for Sport could rage on.
Sarri is hopeful that all the cards can fall in place though, allowing him to sign Kovacic from Madrid. As revealed by Goal, the Croatia star would be keen on coming to west London permanently.
“Yes, Kovacic is only on loan, of course. I'd like very much that Kovacic will stay with us,” Sarri told reporters at Cobham Training Centre. “You know very well that, in that position, we have some problems because we have only Jorginho.
"In my opinion, Kovacic could become a very good central midfielder. Of course, he is not a defensive midfielder but, as you know, in that position I prefer a very technical player. In the last match, Jorginho touched 161 balls.
"So, for us, it's very important for us to have big quality in that position. Big quality not for the last pass, but big quality in terms of moving the ball.
"No [I don't want to buy another midfielder], I want to try with Kovacic.”
Sarri is preparing for his side's upcoming game against West Ham on Monday, as a tense battle continues over qualification for next season's Champions League.
One of the Hammers' top performers this season has been Declan Rice, who, like Blues winger Callum Hudson-Odoi, made his England debut over the recent international break.
Sarri has acknowledged the ex-Chelsea academy player's quality ahead of the upcoming match.
“I think that he's a very good player, very good in the defensive phase because he's really very able to recover the ball," Sarri said of Rice.
"He usually plays very close to the defensive line and, in the first match against West Ham, he was really a very big problem for us.
"I think he is improving in the offensive phase. He has improved during the season because I saw their last matches and I saw a very good midfielder.”
Sarri complained about the Premier League's schedule over the winter period, and has again voiced his concerns over his club's fixtures ahead of a busy week.
Chelsea's game against West Ham has been moved to Monday to be on television, but it means the Blues have less time to prepare for Thursday's Europa League quarter-final first leg at Slavia Prague.
“I am not able to understand the decision of the Premier League because we have to go to Prague as an English team," Sarri said. "So I'm not able to understand why we have to play on Monday. It's very strange.
"Also in the Champions League, the English teams have only three days (to prepare). I think that, in this case, it was easy to solve the problem. But the situation is this, so we have only to adapt to the situation.
"We have to play after three days in Liverpool, so we'll need to change. I think they could have done more for the English teams in Europe. In Serie A, teams play on Friday. Teams involved in the Europa League away from home, they can ask to play their next Serie A match on Monday.
"It's a Premier League decision. And they showed in the last season that they are the best because they are able to sell in the best way English football. This is the situation and we need only to adapt to this situation.”
The Premier League ranks far ahead of rival European leagues in terms of money made through television deals, which allows clubs to sign the world's best players.
Sarri has admitted that it is a beneficial part of being a Premier League manager, but added that he would personally accept a pay cut to improve fixture congestion.
“For me, it's not so important for me, the salary," Sarri said. "So yes, of course. Yes, of course. It is important to have fun, for me. To work without working because, for me, it's not work. For the players, no, because the Premier League is the best championship in the world.
"So we need to have very strong players. But, as I said before, the Premier League was able to sell in the best way possible the Premier League [rights], so in England we are lucky.
"We can buy the best players in the world, we have the best championship in the world, and so we have to accept we have to play every three days.”