The Croatian midfielder hobbled off after really reckless tackle from Leeds United’s Daniel James - who was sent off for his trouble - on Wednesday night.
Kovacic tried to carry on, but had to be replaced by Ruben Loftus-Cheek for the remainder of the game.
After the game, the 28-year-old was seen with a huge strap on his leg, raising doubts over his availability for the Wembley showdown.
But Thomas Tuchel said the Croat has made some progress, and the coaching team will try to give him the best chance to recover in time.
He said: “We have tried today, which is pretty surprising that we are even in the situation to try it, but Mateo wants to try it, and the medical department gave the green light to try it.
“The ligament is already torn from the last incident, so there is no new injury, but he is in heavy pain, and it’s heavily swollen, so we’re hoping time is maybe enough that he makes it.
“We will try it in two-and-a-half-hours of training, and we’ll know more about it.”
Chelsea lost the Carabao Cup final to Liverpool earlier in the season, and will be desperate to turn things around after a rather difficult season.