That's according to the Daily Star, who report that Arsene Wenger was left impressed by the diminutive Porto playmaker after watching him in action at the World Cup for Colombia.
Wenger was in Brazil for French television, and while he had his eye primarily on striker targets for the Gunners, he was also keeping a close watch on the likes of Quintero - talented, young attacking midfielders perfect for Arsenal's system.
His role at Porto
Quintero, 21, was often used as a substitute last season for Porto. He had spent the previous season on loan with Pescara in the Italian top flight, but returned to Portugal to make 22 appearances in the Liga Sagres. Just four of those were starts though.
A strong finish to the season earned Quintero a call-up to Colombia's World Cup squad, where again he was used from the bench as one of his country's primary options in the second half.
Arsenal's Colombian signing
At the World Cup he played alongside new Arsenal recruit David Ospina. The goalkeeper joined the Gunners earlier this week for a £3m fee and will compete with Wojciech Szczesny for a starting place.
A skilful attacking midfielder, Quintero had been mentioned as a target for United as well as a number of Italian clubs after a successful individual campaign in Serie A.
United are now thought to be pursuing other targets, namely Angel Di Maria of Real Madrid and Edinson Cavani from Paris Saint Germain.
Arsenal have plenty of options in Quintero's preferred position, including Mesut Ozil, Santi Cazorla and Alex Oxlade-Chamberlain. But speculation over Cazorla's future, with Atletico Madrid lurking, may have Wenger exploring his options as the summer deadline draws near.