The Spain international has become an instant hit at Stamford Bridge, scoring eight goals in six Premier League matches thus far, despite suffering a recurring hamstring problem.
Chelsea boss Mourinho previously stated that the former Atletico Madrid man was unable to play three games in short succession and that he was doing little training because of his injury.
"Diego Costa will start [against Sporting]," Mourinho said. "Hopefully he plays on Sunday against Arsenal.
"Didier Drogba will be out for a couple of weeks, he has a problem with his ankle and wasn't able to travel."
Mourinho previously worked as a coach and interpreter at Sporting under the legendary Bobby Robson, and the Portuguese would like to see the Primeira Liga side reach the knockout stages with Chelsea.
"I did everything I could at this club," he added. "If I could choose the outcome of this group I'd have us first and Sporting second.
"A good result for us is to win and we will try but Sporting have their weapons."
