Izvestia says both Premier League clubs have been following Doumbia for much of the calendar year and are ready to bid for the striker in January.
CSKA rate the centre-forward at £18 million, which could prove too rich for either English outfit.
Former CKSA star Rolan Gusev said: "Of course, a player like Doumbia, could not fail to attract attention in Europe.
"He's achieved great results with CSKA."
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