The Ivorian was taken off with an ankle injury during Sunday's pre-season friendly against Ferencvaros but the club are confident that the problem is not serious.
"He's good," Mourinho told reporters of Drogba after his side's 2-0 win over Real Sociedad on Tuesday night.
"I don't want to say [he will be] ready for Monday but, with the quality of our medical department and the mentality he has, I'm not saying it's impossible for him to recover for Monday."
Despite the Blues icon's return to Stamford Bridge this summer, though, Drogba is set to play second fiddle to new signing Diego Costa, who scored both goals against Sociedad, and Mourinho is thrilled to have pried the striker from Atletico Madrid.
"What can we expect? I expect Diego and Diego is a team player who works hard, he's not just about goals," the Portuguese enthused of his €44 million purchase.
"It's about his defensive work, mentality and ambition. This is the player we bought and we were waiting for since last season. This is why we didn't buy a striker in the winter market. We were waiting for him, we have him and hopefully everything goes well.
"He looks adapted to the team and the Premier League - not just Chelsea - should be happy. Sometimes we lose important players going to other countries and sometimes we bring new top players here.
"You can consider that [a bargain] because the market is crazy and the values are very high. For a striker like him, a champion in Spain, a Champions League finalist, a 25-year-old, we consider the price was very much in our favour."