The 26-year-old was omitted from the Blues’ matchday squad for Tuesday’s 6-0 hammering of Maribor in the UEFA Champions League.
Reports in the English media claim that Costa, who finally opened his La Furia Roja account in their 4-0 win over Luxembourg on Sunday, was admitted to hospital to treat his illness.
The west London club have not issued any statement on the matter, although the prolific marksman is rated doubtful for the trip to Manchester United on Sunday.
The Spain international has made a flying start to his career at Stamford Bridge, scoring nine goals in just seven Premier League appearances for Jose Mourinho’s side.