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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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
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