The Daily Mail reports that United are set to rival Spurs in the chase for the 22-year-old striker.
Internacional rejected an £15million bid from Tottenham for Damiao in the summer.
The Brazilian side is reportedly looking for around £24million for the highly-rated striker.
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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.