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However, rivals Manchester City are also said to be in talks for the highly-rated 18-year-old.
Henriquez was already in Europe, as he is with Chile's youth squad who are playing in numerous friendlies, including the Milk Cup in Northern Ireland.
United have been tracking Henriquez for months and he has already trained with the club, but reports in England claim City want him too.
However, Chilean sources say he is set to join United.
Universidad de Chile's assistant manager Sebastian Beccacece was asked about Henriquez.
"No doubt he is a very useful player, with a good goalscoring talent," he told Radio ADN. "But we have to count on the players that we have available, not the ones that aren't available."
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