Whether it comes at Palace or against Roma remains to be seen.
Kante was superb last season as Chelsea won the Premier League, and has been a steady performer so far this campaign.
Morata picked up a hamstring issue in the loss to Manchester City just before the two-week global break.
However, according to The Telegraph, Kante could miss Chelsea's next six fixtures, which includes their double-header with Roma in the Champions League. Given his tenacity and ball retaining quality, the Blues are widely expected to struggle in the wake of the problem sustained.
Kante had been an ever-present in the top flight this season, but the former Leicester City man faces the possibility of missing at least three league games in the coming weeks. It is more likely Tiemoue Bakayoko and Cesc Fabregas will be deployed in midfield from the start, but defenders Andreas Christensen and David Luiz - back following suspension - are alternative options.
Initially, it was thought that Kante wouldn't be out for that long but he has since been assessed by Chelsea's medical staff and the conclusion is worse than first thought. The hope now is to have him fit and available for the welcome of Manchester United next month, but that's a double-edged sword on its own.
The global break is basically over, but it didn't quite go exactly to plan. He's now being evaluated by Chelsea's medical staff, but reports earlier this week from France were expecting him to be out at least as long as Morata (2-3 weeks), if not longer (all of October and maybe a day or two extra).