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The club reportedly granted the 29-year-old compassionate leave after he raised concerns about his health and safety. Kante's brother Niama died of a heart attack just before the 2018 World Cup, and the midfielder himself fainted during a training session that same year. Cardiology tests didn't reveal a heart issue.
Chelsea striker Tammy Abraham also expressed fears about a return to training. His father Anthony suffers from asthma.
Manager Frank Lampard supported Kante's decision to stay away from Chelsea's Cobham base. There were suggestions the Frenchman would miss the remainder of the campaign, but that now seems unlikely.
Kante trained away from the rest of his teammates, according to The Telegraph's Matt Law. Earlier in the week, the Premier League gave clubs and players permission to tackle during training. Players and staff will continue to be tested for the coronavirus twice each week.
The Office for National Statistics released figures in May indicating black men and women are nearly twice as likely to die from COVID-19 as white people in England and Wales.