Now 18, the exciting attacking talent can move freely to Europe, but while he is linked with the likes of Real Madrid, Inter Milan and Borussia Dortmund, United have first option on the youngster until 2014 thanks to an agreement struck with 'U' almost three years ago for the then 15 year-old.
Henriquez has already spent two trial periods at United's Carrington training complex in the last two years and will continue to visit annually until the English giants decide he is ready to make the big leap.
"The idea of the people of Manchester is that I begin my senior career with U. I'll do my development process here and I go when I have a little more experience," says the teen, who is now a virtual first-choice at U under highly-rated coach Jorge Sampaoli.
U president Federico Valdes insists no cash has changed hands, instead United will monitor Henriquez's development closely before shelling out a fee when they feel he is ready.
"It is untrue that there is a concrete offer," says Valdes, "but they are very mindful of what he can do and are monitoring him closely."
There is talk of United having a pre-agreed €4 million option for Henriquez, though Valdes hints it could be more.
Indeed, he could go for more than Sebastián Rozental, who remains Chile's biggest teenage transfer when he left Universidad de Catolica for Rangers over 15 years ago.
"I do not know how old he was and how much it cost Rozental when he left. He was 19 and went for $6 million? Then he (Henriquez) will be more expensive than Rozental."
Henriquez is now making headlines for U, winning the club's Player of the Month award last month and now thriving under the tutelage of Sampaoli, who is regarded highly by United manager Sir Alex Ferguson.
"The Manchester United people say they would prefer I continue playing here," says Henriquez. "Playing for United would be a dream come true, but I know to get there I must work hard and play well here.
"No-one has told me anything different. So I stay and will keep working hard for U.
"It would be very rare if I went to Manchester at my age. They said they would sign me once I am older and gained more experience."
Such has been Henriquez's progress this season that he's forced senior attacking teammates to the bench and led one, Peru international Raúl Ruidíaz, to consider openly whether he needs to leave to find regular first team action.
Now running around in the U No8 shirt, Henriquez can play as an out-and-out striker, but also on either flank and has the ability to play behind a centre-forward in a true No10 role.
But for all his talent, Henriquez could easily have been lost to football just two years ago.
The Chile youth international had to choose between football and tennis as he started to become involved in U's senior squad.
He played at the same club as Chilean tennis star Fernando Gonzalez and admits he could've turned pro.
"I was going to become a professional, but I got bored. Tennis helped me in developing my pace and agility," he says.
Sport runs through the Henriquez family, with older brother César "Cuqui" Henríquez a star with Palestino. Indeed, United fans may owe Cuqui as it was watching his older brother make his way in football that convinced Henriquez to change sports.
"I was doing well with my school team and U made contact," recalls Henriquez. "I thought I could make it there, so I agreed to join."
Even if United didn't boast their first refusal agreement, England would still be the favoured destination for Henriquez, as he confesses he grew up idolising Arsenal legend Thierry Henry and former Old Trafford hero Ruud van Nistelrooy.
"My favorite player is 'Titi' Henry, but I'm more like Ruud van Nistelrooy," he says.
If the move does happen for Henriquez, modeling his game on the Dutch legend wouldn't be a bad start for United's latest South American transfer target.