The Blues have opened talks with the Ivory Coast ace - who becomes a free agent in 12 months - over a one-year extension to his current deal.
The length of the new contract has proved a sticking point as Drogba's representatives have so far insisted on a three-year deal.
He has been disillusioned after losing his starting place to misfiring Torres - who only scored one goal in 18 appearances last term - in key games at home and in Europe.
Drogba had an offer from Galatasary on the table and a megabucks move to the MLS and Qatar were also mooted.
Tottenham boss Harry Redknapp is keen to add firepower to his front line and is also believed to be sniffing around.