Both the Times and Guardian newspapers reported that Kante had twisted his knee during a training session on Saturday and was not likely to recover in time for the final.
The 28-year-old's absence is a blow for Sarri, who is already without the services of defender Antonio Rudiger, midfielder Ruben Loftus-Cheek and winger Callum Hudson-Odoi due to injuries.
(Reporting by Simon Jennings in Bengaluru; editing by Amlan Chakraborty)