Speaking after Chelsea's 3-0 victory over Aston Villa at Stamford Bridge on Saturday, in which Costa struck his eighth goal of the season, Mourinho revealed the Spain international barely trains in between matches to protect his tight muscle.
Costa's form in the Premier League has helped Chelsea pull three points clear at the top of the table but his injury has ensured he has only been able to start one match a week.
That scenario is far from ideal given the club's UEFA Champions League commitments and Mourinho has targeted the next international break as a chance for the 25-year-old to fully recover from the problem, providing he is not called up by Spain coach Vicente del Bosque.
"A striker scoring goals is always nice for him and for his confidence," said Mourinho after Saturday's victory. "Especially for someone like him who is not training as he should because we are protecting him in certain situations so he cannot be at the top of his game.
"He's doing almost nothing [in training]; he's resting and recovering from the tight muscle he has every time he accumulates fatigue.
"I think if he doesn't go to the national team and stays here for 15 days just on treatment and recovering, making the muscle and the areas around the muscle stronger, he has the perfect chance to be top for Chelsea and [his] national team.
"If he doesn't have this period he will always play one game [but] the next is trouble. The muscle is tight; the muscle is in danger to rupture.
"We have to respect the decisions [of Del Bosque] because we can't do anything [to stop him being called up]."
Costa has been struggling with the problem since the end of last season and aggravated the injury during the last international round of fixtures, forcing him to miss Spain's win over Macedonia in Euro 2016 qualifying.
