Drogba, who is out of contract following a stint with Turkish side Galatasaray, reportedly has a lucrative two-year contract offer on the table from Italian champions Juventus.
But the Ivorian, who scored 157 goals in 341 appearances for Chelsea, is said to be leaning towards returning to London to once again work under Jose Mourinho.
The 34-year-old remains the only player in history to have scored in four FA Cup finals and is idolised by the club’s fans.
Mourinho signed Drogba for £24m from Marseille in 2004 and together the pair won six major trophies including the Premier League in their first season, Chelsea’s first top-flight title in 50 years.
Drogba went on to win another six trophies after Mourinho left the club in 2007, including the Champions League.
Chelsea have already completed the signing of another striker in Diego Costa, who completed a £32m transfer from La Liga champions Atletico Madrid earlier this week.
But Samuel Eto’o has already left the club following the expiry of his contract while another striker, Demba Ba, completed a £5m move to Besiktas on Friday.
Romelu Lukakau, who spent last season on-loan at Everton, has been linked with a move away while Fernando Torres has failed to convince in a Chelsea shirt since his £50m move from Liverpool in 2011.