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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The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.
Five English clubs will compete in the last sixteen of the Champions League for the first time ever as Liverpool, Manchester United, Manchester City, Chelsea and Tottenham face some difficult away matches.