Over three and a half seasons with Arsenal following his £35 million ($44 million) move from Barcelona -- where he had to make way for the arrival of Uruguay's Luis Suarez from Liverpool -- Sanchez built a reputation as one of the most feared forwards in the Premier League.
He was twice voted Arsenal's player of the year and featured in the 2014/15 Premier League team of the year.
Sanchez sends Chile into Copa America quarter-finals
But in his 18 months with United, Sanchez has lost both form and confidence, and now the Premier League giants are reportedly desperate to offload him and his reported £400,000 a week salary.
Yet Sanchez has shown signs of his old self at the Copa America, where he scored the winning shoot-out penalty against Colombia to send Chile into a semi-final meeting with neighbors Peru.
He also scored in each of Chile's opening two matches, victories over Japan and Ecuador, meaning he's scored more times in this month-long competition than he did in the entire Premier League campaign for United.
According to Rueda, it boils down to one thing that is missing from his life in rainy Manchester: "love."
"In the national team and because of the attention they receive, the players don't want to leave," said the Colombian coach, who is no fan favorite himself due to leaving out popular goalkeeper Claudio Bravo from his Copa squad.
"Despite not playing for their clubs, they come here with commitment and forge a strong group."
Sanchez is a hero in his country having been one of the stars of Chile's back-to-back Copa America victories in 2015 and 2016 -- the only ones in their history.
He's known as the "Nino Maravilla" -- the Wonder Kid -- in his homeland and is Chile's record goalscorer with 43. There's even been a film made about his life, in which he starred.
As well as scoring the winning penalty against Colombia, he netted the decisive goal in the 2-1 victory over Ecuador, and helped blow out the scoreline late on in the 4-0 thumping of Japan.
In Manchester, he managed just one Premier League goal in 20 appearances, although only nine of those were from the start.
He looked lost most of the time in the red shirt of United, rarely able to link up effectively with his team-mates or produce any of the pace and trickery that was a feature of his career at Udinese, Barcelona and Arsenal.
But he's not alone in putting behind him disappointing club seasons to thrive with his national team.
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Colombia's James Rodriguez, seemingly unwanted by either his parent club Real Madrid or Bayern Munich, where he spent the last two seasons on loan, was all creativity and ingenuity with Colombia in Brazil until they lost to Chile.
And Philippe Coutinho, jeered by Barcelona's fans and pilloried in the notoriously demanding Catalan press, scored a brace in Brazil's opening match against Bolivia and remains an unconditional starter in coach Tite's team.
But while they can be under-appreciated at their European clubs, they remain adored by their countries' fans.
"That's why players like Coutinho, James or Alexis, who didn't have a great season, become themselves again with the national team," said Rueda.
"The treatment that is given to the players as professionals and as people generates the reciprocity that allows them to give their all."
In his current form, Sanchez looks not only capable of leading Chile to an unprecedented third straight Copa title, but is putting himself in the shop window to earn a move to one of Europe's giants and end his United nightmare.
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