The 37-year-old striker has led the Premier League leader's attack in wins over Queens Park Rangers and Manchester United in recent weeks due to Costa's hamstring injury and Remy's calf problem.
Drogba, a United Nations Development Programme Goodwill Ambassador, on Monday withdrew from featuring in the Match Against Poverty in St Etienne.
It is not the first time Drogba has had an ankle problem this season.
He has made five Premier League starts this campaign, but could be displaced in Chelsea's starting line-up at the Emirates Stadium anyway if Costa or Remy is fit.
"Our target was for Diego to play the last four matches and Arsenal is the sixth match from the end," Mourinho said last Friday.
"He starts training with rest of the squad next week."
Mourinho also reported Remy had a better than 50 per cent chance to play against United, although teenager Dominic Solanke was on the substitutes' bench, with the France striker ruled out.
Chelsea is 10 points clear of the second-placed Gunners and victory against Arsene Wenger's men will mean the Blues can wrap up the title at Leicester City three days later.
