The British tabloid newspaper reported that Costa had been fined for a bust-up with manager Antonio Conte, amid reports of a potential move to China.
The Brazil-born Spain international was left out of Chelsea's squad to face Leicester on Saturday, but the club claimed that the striker was suffering from a back injury.
A source from Chelsea Football Club has since denied reports that Costa was made to pay a £185,000 fine for his part in the alleged bust-up.
"We don't fine players when they injure their backs," the figure told 'Sky Sports News'.
The 28-year-old has reportedly made up with Conte and will be in contention to face Hull on Sunday.