News of the World says Blues owner Roman Abramovich has put an end to the club’s free-spending era.
Drogba and Cole have just 18 months left on their current contracts.
A Blues source told News of the World: “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.”