But, should Costa not be fit enough to face Arsenal, Mourinho made it clear that he definitely will be ready for Chelsea's match against Leicester City on Wednesday.
Costa has missed Chelsea's last two games after aggravating a hamstring injury, but it seems that he is likely to play on Sunday, especially since Loic Remy's chances of doing so are dwindling.
"Didier [Drogba] for sure is good, is fine," Mourinho said during a press conference. "Remy not for sure. And Diego… let's make a decision tomorrow.
"He's a very important player for us, but the reality is we are coping with the difficulties of every match without him. Remy did well for us; Didier is doing well for us. The team is playing in a different way to adapt to those two, but we are doing our job.
However, Mourinho made it clear that even if Costa doesn't play, he has faith in his other strikers to get the job done.
"We played amazingly well during the most part of the season, scoring a lot of goals and controlling games very well through the quality of our possession," he said. "In the last period we are more strategic, less artistic, but we are having results. I would love Diego to be back, but I trust the other people."
Mourinho also hinted that 17-year-old striker Dominic Solanke might play against Arsenal, should Costa not be fully fit.
"This week, because we are not sure about him, we decided [Dominic] Solanke wouldn't play yesterday with the under-21s, also to have him fresh and ready," he said. "Didier and Solanke, or Didier and Diego. We make that decision tomorrow. But Diego is there for Leicester if not Arsenal."