Jose Mourinho’s move for the Spain international is virtually complete, but has been held up by the striker’s hamstring injury.
Personal terms with Costa have already been agreed, but his hamstring complaint has delayed the player’s Stamford Bridge medical.
But Costa has returned to training ahead of Spain’s attempts to retain the World Cup in Brazil and Chelsea will now press ahead with plans to complete the mega deal.
Costa will become Chelsea’s first major signing of the summer, but the Blues are facing a fight to keep Eden Hazard from the clutches of Paris St Germain.
The French club are preparing a £60million bid for the Belgian international this summer – a fee that could be too good to resist.
Chelsea want to keep the talented forward, but PSG believe they Hazard wants to join them and can be lured away from West London.