Costa has been plagued by the problem throughout the season since arriving from Atletico Madrid, and has had to be closely monitored by the Premier League leaders to keep him on the pitch.
The striker – who has scored 19 goals in the league this season – was forced to withdraw from Spain's recent squad as the problem flared up again but Mourinho is confident they can manage and improve the situation going forward.
"He will continue to work the way he does to prevent it, to make the muscle stronger but still elastic and flexible," said Mourinho.
"We don't believe in operations, I always believe it is the last decision for every injury, we try to be conservative, to train, recover and work, we don't believe will go the surgery direction.
"Diego trained yesterday and today, he's not injured. I don't know if I will start with him or not because with a muscular injury you need to analyse situation with him.
"He has had no days off and has been working hard. We did all the tests to confirm two days ago that the muscle is fine, now he needs confidence that it won't break and he is free to express himself at the maximum intensity."
Meanwhile, Mourinho believes four teams are still contesting the title and has his sights firmly set on the 86 points they need to finish as champions.
"Given the points difference you have to say four [teams are in the running]," he added. "It makes me feel they are [all] there.
"We need six victories and one draw in nine matches so it's a good situation for us, it is a situation all the other clubs would like to be in.
"But I am not thinking about how or when [it happens]. I don't care where we win it, if it's in hotel, away or at home, I just want to win it."
Get the best features, fun and footballing frolics straight to your inbox every week.
Thank you for signing up to Four Four Two. You will receive a verification email shortly.
There was a problem. Please refresh the page and try again.