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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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.