Costa took his season's tally to eight goals as Chelsea remained top of the Premier League with a 3-0 win over Aston Villa at Stamford Bridge on Saturday.
But the fitness of former Atletico Madrid star Costa, who has been struggling with a hamstring problem for several weeks, remains a concern for Mourinho.
The Chelsea manager believes Costa needs a rest to protect his hamstring and revealed how he is not taking full part in training as he nurses him through the season.
In the circumstances, Mourinho insists his Spain forward can only play one game a week, but he could yet utilise him for Tuesday's Champions League game at Sporting Lisbon -- a fixture Chelsea can ill-afford to lose after drawing their group opener against Schalke.
"Diego's doing almost nothing. He's just resting and recovering from the tight muscle he has every time he accumulates fatigue," Mourinho said.
"I think if he doesn't go to the national team, and stays here for 15 days of treatment, recovering, and making muscle and the other areas around muscle stronger. I think he has perfect chance to be top for Chelsea and the national team.
"If he doesn't have this period, he will be always play one game and the other game he is in trouble. The muscle is in danger of rupturing."
Even on one leg, Costa proved too strong for Villa. Chelsea led via Oscar's early goal but Villa handed the hosts numerous scares before second-half goals from Costa and Willian sealed the win.
Mourinho insists being top of the table counts for nothing at this stage. But leading from the front is a position that sat comfortably with him during his first trophy-gathering spell in charge at Stamford Bridge.
"Not to lose many points at home during the season always becomes important factor," Mourinho added.
"We are playing well, scoring goals and we are happy. But we go match after match. The next one for us in the Premier League is Arsenal.
"We have a lead of three points over Southampton, which give us a guarantee that next weekend we will still be top of the league. This is very, very important.
"It's not crucial because it's too early. But it's a little bit of space. And it gives you a good feeling that you are top of the league.
"I think everybody knows that everybody is going to lose points. Nobody is convinced Chelsea is going to keep this run for 10 or 15 matches, getting positive results.
"We know this Premier League. Everyone knows it's possible for top teams to lose points."
Aston Villa's early-season fixture list has not been kind on boss Paul Lambert and it won't get any easier with a game against Manchester City, the Premier League champions, next up.
However, the imminent return to fitness of Belgium striker Christian Benteke after a six-month absence with an Achilles injury will provide a welcome boost.
"We are playing without a recognised striker at the moment. That does not make it easy," Lambert said.
"We are also in a run of games that is really tough. You are playing against top sides. You know it's tough and we are up against Manchester City next."