The reports did not name the players and Chelsea did not immediately respond to a Reuters request for comment.
Players who test positive have to self-isolate for 10 days and return a negative coronavirus test before they can take part in training.
Sheffield United, Brighton & Hove Albion and West Ham United were among the other English Premier League (EPL) clubs to report positive COVID-19 cases in recent weeks, the Times said.
Frank Lampard’s side, who finished fourth last season, kick off their campaign against Brighton on Sept 14.(Reuters/NAN)