Striker Costa has served his three-match Premier League ban for stamping on Liverpool’s Emre Can, and will return to the starting line-up when Jose Mourinho’s men travel to Paris.
Jose Mourinho said: “Yes, I start him. But I don’t think it’s good for a player to be three weeks or three matches without starting a game. So I don’t think he’s in the best of his condition.”
The only member of the squad missing from pre-match training on Monday was midfielder John Obi Mikel, who remains troubled by a knee injury.
Oscar (muscular injury) should be fit to feature as the Premier League leaders look to find an away advantage on Tuesday night.
Mourinho has decisions to make in goal, with Petr Cech and Thibaut Courtois in contention, and central defence, where Kurt Zouma could continue ahead of Gary Cahill.
French champions Paris Saint-Germain are suffering an injury crisis ahead of the first leg.
Manager Laurent Blanc was left exasperated by his side spurning a 2-0 lead with 88 minutes played to draw 2-2 at Caen at the weekend, and his mood will not have improved as his players piled up in the treatment room.
Yohan Cabaye, Marquinhos and Serge Aurier all went off injured during the draw, while winger Lucas had a groin problem. David Luiz is expected to face his former side for the first time after leaving in a £50million summer deal.