There is no guarantee that England's top flight will be allowed to safely resume in the coming weeks, although it is being widely reported that the league could return before the end of June.
Kante trained with Chelsea on Tuesday but allegedly missed the club's sessions on both Wednesday and Thursday due to concerns over spreading the disease to his family.
According to Sky Sports News, the France international is prepared to miss the rest of the season and 'has the full support' of head coach Frank Lampard, in addition to the club's board.
The 29-year-old has had his injury problems this term but has still featured on 22 occasions for his London club in all competitions, including 18 outings in the Premier League.
The Blues are currently fourth in the Premier League table, three points clear of fifth-placed Manchester United, who have also played 29 of their scheduled 38 matches this season.