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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Chelsea have struggled to build momentum in the opening stages of the campaign and are currently looking over their shoulders at the relegation zone.
Who of Europe’s top strikers will move to England this summer?