The Blues striker has been suffering from a long-term hamstring problem and was doubtful for last week's 6-3 win at Everton, but still played for Jose Mourinho's side and contributed two goals.
Costa has started his Stamford Bridge career in fine form netting four times in three Premier League matches, and it will be a huge blow to Chelsea if the marksman is ruled out for any length of time.
Liverpool striker Daniel Sturridge admits he is "heartbroken" to have been ruled out of action for the next three weeks with injury, after confirmation he'll miss England's Euro 2016 qualifier against Switzerland on Monday.
The 25-year-old suffered a thigh strain in training this week and is also likely to miss two Premier League games as well as Liverpool's first Champions League match against Ludogorets Razgrad.
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