The Telegraph says Kante passed out after a training session on Friday as Chelsea prepared for Sunday's match at the Etihad, which they lost 1-0.
His team-mates feared he had suffered a heart problem when he collapsed in front of them.
A Chelsea medic is said to have rushed quickly to the scene after the incident occurred in the dressing room. Having regained consciousness and received treatment, Kante had cardiology tests, which came back clear.
The 26-year-old was cleared by a specialist to play against City but he felt unwell on Sunday morning and it was decided that he would not be risked.