The News of the World says despite having just 18 months of their current deals to run, both Drogba and Cole have been told there will be no talks until the end of the season.
It is another sign Roman Abramovich has closed the door on the era of Chelsea’s free-spending.
But boss Luiz Felipe Scolari has told his stars they’d be “mad” to think about quitting the Bridge.
Drogba, Florent Malouda, Wayne Bridge, Paolo Ferreira, Juliano Belletti and Alex have all been linked with moves.
But a Blues source said: “Scolari realises the impact the change in the economy will have on football.
“And that’s why he has told his players they’d be mad to think about moving away from here.
“He reminded them that they are at a great club, a successful club and a sound club.”