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."
Borussia Dortmund hears Wembley Calling and are headed to London for the Champions League final.
Chelsea won the Europa League on Wednesday. The Blues defeated Benfica 2-1 on injury time goal from Ivanovic.
The Juventus jersey for the 2013/14 was released earlier this week. Be the first to wear the colors of the Old Lady.
The adidas Nitrocharge is the most talked about new cleat in years. It was released on May 15 and will take your pitch by storm.
One of the top soccer cleats for control the Nike CTR360 will not let you down on the field in tight spaces.
Bayern Munich are kings of Germany and hope to be crowned kings of Europe at Wembley later this month!
The push for more color on their cleats, adidas has added the infrared colorway to the adiZero f50 Line.
adidas has added some color to the Predator line with this new colorway. Released on May 17. Be the first to own a pair.
The Liverpool 2013/14 soccer jersey is available for pre-order. The Reds are eager to compete for silver next season.
The new PUMA evoSPEED 1.2 FG. A great new soccer cleat with classic look and first time for PUMA to be on the cleat.