Tottenham failed with a £20million bid for Damiao last week.
The striker was offered to Liverpool on loan, but the Reds were not prepared to pay the fees Internacional demanded.
The Daily Mail reports that United held talks with the striker in February and intermediaries met his representatives in Brazil on Monday.
United have reportedly outlined a proposal for January.
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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.