However, the new Blues manager would first need to get permission from the striker's current club Galatasaray.
According to The Mirror, Drogba visited the Chelsea training ground last week.
Mourinho and he are reported to have discussed the possibility of Drogba returning to Stamford Bridge and both parties are keen to make it happen.
Galatasaray, though, want the 35-year-old to see out the remaining 12 months of his contract. If that happens, then Mourinho would still want Drogba to return next summer.
Chelsea made an approach to re-sign Drogba back in January but lost out to the Turkish side.