Scolari wants funds to rebuild the squad and, according to The Sun, has told owner Roman Abramovich the Ivory Coast international can go.
Chelsea want £22million, with AC Milan desperate to get Drogba after missing out on Arsenal's Emmanuel Adebayor.
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Clearout: Drogba could make way for new faces at Stamford Bridge
And Scolari has also offered Florent Malouda to Barcelona as part of an £18m bid for striker Samuel Eto'o.
Having landed Deco on Monday, Scolari aims to shake up his squad and is keeping tabs on Ronaldinho, who Milan also want.
But Barca team-mate Eto'o, 27, has become top target.
He wants £160,000-a-week but the Blues are confident signing-on and loyalty bonuses will reduce his wages.
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