Costa has missed the Blues’ last two games with the injury and is a doubt for the Emirates showdown.
However, Mourinho has confirmed he will give his star striker as much time as possible to prove his fitness ahead of Sunday’s 4pm kick off.
Chelsea have won four league games on the bounce and have drafted in 17-year-old striker Dominic Solanke as a replacement for Costa if they Spain international cannot start.
Fellow forward Loic Remy (calf) is out but veteran Didier Drogba is fit following an ankle knock.
Mourinho said of his striker shortage: “I would love Diego to be back but I trust other people.
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Jose Mourinho's Chelsea face Arsenal at the Emirates this weekend
“This week, because we are not sure about him, we decided Solanke shouldn’t play yesterday in the U21s so we could have him fresh and ready.
“I don’t know if we’ll play Solanke or Didier and Diego. We’ll make that decision tomorrow.
“Diego, if not Arsenal, he’ll be back for Leicester.”
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