The 36-year-old forward is currently without a club after leaving Galatasaray, and is rumoured to be attracting interest from Juventus and side in the Middle East.
But Jose Mourinho is ready to make a stunning move to get him back to west London as he plots to boost his attacking options.
The Blues have recently signed Diego Costa, but with Demba Ba set to follow Samuel Eto’o out of the club, ‘The Special One’ will have only the Spaniard and Fernando Torres to rely upon.
Drogba is a hero at Stamford Bridge after signing for them in 2004, and his last kick for the Londoners was a Champions League-winning penalty in 2012.
Teams in Qatar are willing to offer him a more lucrative deal, but Mourinho is hopeful that his relationship with the Ivorian may be the deciding factor.
Drogba won three league titles, four FA Cups and the European Cup with Chelsea, and is widely hailed as one of their best ever strikers.