Chelsea head coach Antonio Conte insisted Costa missed Saturday's Premier League win at Leicester with the injury, refusing to comment publicly on a rumoured falling out amid reports of a big-money bid from China for the Spain striker.
And having missed three days of training and subsequently undergoing treatment, Costa returned to the training pitch for a solitary session on Sunday and Monday.
Conte, his staff and Costa's team-mates will return following two days off on Tuesday, but Chelsea insist the 28-year-old's solitary sessions are part of his recovery and nothing to do with the speculation over his future.
Costa, who has scored 14 Premier League goals in 19 appearances this season, will be evaluated again on Tuesday to determine if or when he can rejoin first-team squad training.
Chelsea, who have a seven-point lead at the top of the Premier League, next play at home to Hull on Sunday.
Costa felt pain in his back last Tuesday, Conte said, prompting his absence
Conte said on Saturday: "If there is a problem - and I repeat 'if' - with the players then in my career I prefer to sort the problem in the changing room, not outside and not in press conference
But I repeat - if
I have told the truth."
Earlier this month Costa was linked with a move to the Chinese Super League, with the accompanying astronomical wages.
It was rumoured Tianjin Quanjian were prepared to bid Â£80million and Costa's future could be the main talking point of the winter transfer window, which closes on January 31.
One potential complication is that China's transfer window closes on February 28.
Although regulations over the recruitment and use of foreign players have been tightened in the Chinese Super League ahead of the season start in March, it is rumoured that Tianjin have an available slot in their squad.
Costa signed a five-year deal on his arrival from Atletico Madrid in July 2014 for Â£32m, so has two-and-a-half years to run.
Chelsea and owner Roman Abramovich would resist Costa agitating for a move, with many pundits insisting the striker is integral to Chelsea's push for the title.
Source : PA