The paper adds that Bayern Munich striker Mario Mandzukic and PSG ace Ezequiel Lavezzi are also on Jose Mourinho's radar.
Drogba left Chelsea in 2012 as a hero after scoring the winning penalty in their Champions League final victory over Bayern Munich. The Ivorian joined Chinese outfit Shanghai Shenhua before promptly joining Turkish outfit Galatasaray, with whom he played against the Blues in the Champions League last season.
Chelsea's £32 million deal for Diego Costa is nearing completion and it seems as though Mourinho has turned his attention to finding further reinforcements in attack - and the Telegraph claim that Drogba could well be the man for the job.
The Special One was the man who brought Drogba to Stamford Bridge from Marseille in 2004 and the pair share a close relationship.
"I think destiny will (see him return). Not even destiny, I think a collective desire from the club and from Didier means that one day, sooner or later, as a player, a coach, as an ambassador, as a board member, and because of the respect between him and owner," Mourinho said in March, ahead of the striker's return to Stamford Bridge for the last-16 Champions League clash.
The 36-year-old is out of contract with Galatasaray and free to join another club.