The midfielder has not played for the Blues since a 4-1 win over Crystal Palace on April 10.
He trained on Friday in the hope of perhaps being available for Saturday's Premier League clash with Fulham.
But he now looks set to miss that game and is a doubt for the second leg of the Champions League semi-final, with Chelsea holding an advantage on away goals after a 1-1 draw in Spain.
Asked about Kovacic's availability at a pre-match media conference, manager Thomas Tuchel replied: "He is still injured, he trained with us, he felt something at the end of the training so he's still not available.
"All other players are available except for Antonio Rudiger who got injured in the last minute of the Madrid game.
"Before today, before training we thought Kova had a big chance to join us at the latest for Madrid, so now we have a little setback, not a big one.
"With him I don't want to be too negative, let's see how he feels tomorrow and for Toni I'm quite positive for Wednesday."
Chelsea, who are three points clear of fifth-placed West Ham, can ill-afford to let up as they fight for a top-four finish that would secure their Champions League place for next season while aiming to win it this term.
After the Fulham game, Tuchel's men have the second leg against Madrid and then face Manchester City and Arsenal prior to the FA Cup final with Leicester City on May 15.
Tuchel conceded it can be difficult to find balance in his team amid such a hectic schedule, adding: "We are in the middle of the race, is it always easy to switch from one competition to another? No, but who cares?
"Everybody can do easy. It's our job to switch focus and it's my job to find the mix, to put the players in the right mindset and to prepare this match in the way that everybody understands the importance of the match.
"We did not work that hard, and I hope the players feel the same, they did not work that hard all these weeks, all these matches to give us this advantage just to let it slip through our hands by not being focused.
"It's [the schedule] brutal honestly. We played in France [at PSG] the same amount of games, two cups and also 20 teams in the league so we got the impression. But, of course, the intensity of the league, the challenge of the league is very, very different now here.
"It is another level, it's quite relentless. But it keeps you on your front foot and it keeps you coming out of bed early. There is simply no time to breathe, there is no time to sit back and get too relaxed or comfortable. This is a good thing, it sharpens your mind, it sharpens your mentality.
"This is what I find very impressive in this club, everybody is on the front foot, everybody in the club is fully aware of what it takes to be in shape, this is very impressive and that's why, although it's super demanding, we feel very comfortable because we arrive any game with the knowledge and deep conviction that we are prepared for this, we can perform at this level and we can adapt."