The North Londoners have a weakness up front with Emmanuel Adebayor on African Cup of Nations duty and Jermain Defoe struggling with injury.
The club have long been interested in Damiao and will now look to see if it is possible to sign the Internacional forward before the end of the transfer window.
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Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.
Newcastle United are staring down the barrel of relegation to the Championship for the second time in the past eight years.