The 18-year-old striker arrived at Old Trafford in September, and has since gone on to score for Chile on his international debut against Serbia in November.
However, the teenager has not yet managed to break into Sir Alex Ferguson's first-team plans and is therefore set to join the Latics on a temporary basis in January.
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"Angelo is as good a goalscorer as you will find," the Spaniard told the Daily Mirror. "He scored goals at Universidad de Chile and he is going to score goals here.
"I am sure he will be an important player for United.
"We are glad we can work with him and he can use Wigan as Tom Cleverley did and adapt to what is needed in this league."
Martinez has already been busy ahead of the month-long transfer window in the New Year, securing the services of Honduran midfielder Roger Espinoza, who is out-of-contract with MLS side Sporting Kansas City on January 1.
The former Swansea manager has also made it clear that he intends to add further to his squad, both to cope with the numerous injuries they have suffered and in order to make his first XI more competitive.
Wigan have struggled in the Premier League thus far and sit in 18th place in the table, level on points with 17th-placed Southampton but in the drop zone due to a worse goal difference.
Next up for the Latics is a home tie against Arsenal, who travel to the DW Stadium in search of a second consecutive win that would see them climb into third position.