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The 28-year-old was a target for Tianjin Quanjian but any potential move was scuppered by new rules in the Chinese Super League, according to the club's owner.
Costa did not play in Chelsea's win at Leicester on Saturday with boss Antonio Conte saying he had a back problem.
He trained on his own on Monday but this was to aid his recovery.
BBC Sport understands Chelsea are determined to keep Costa, who is the joint top scorer in the Premier League with 14 goals.
Costa's return to training means he could be in contention for the visit of Hull on Saturday as Chelsea look to extend their seven-point lead at the top of the table.
Chelsea striker Diego Costa trained with the first team on Tuesday after being linked with a move to China.