The Scot travelled to the Spanish capital to assess the 21-year-old midfielder, who only signed a contract extension with the Rojiblancos during the summer
The Scot, who is still looking to add more creativity to his midfield at Old Trafford, was given a VIP seat by the Rojiblancos and spoke to the club's sporting director, Jose Luis Caminero.
"I suppose he came to see us because Atletico are a Champions League team and because they also qualified for the last 16," the former Spain international told Canal Plus after the game.
"We spoke, but he didn't tell me exactly why he had come ..."
Koke played the 90 minutes as Diego Simeone's men, who had already qualified for the last 16, won their final group-stage fixture 2-0 thanks to goals from Raul Garcia and Diego Costa.
The 21-year-old has scored 10 goals in 134 games for Atletico and has also represented Spain on seven occasions, after making his debut for La Roja earlier this year.
The midfielder recently put pen to paper on a new deal at the Calderon to extend his current contract to 2018 and told Canal Plus: "I didn't know anything [about Moyes being here], but I'm not concerned [with any of that]. I renewed in the summer."
United have been tracking Koke for several months and believe he fits their profile as a potential signing due to his age, outstanding technique and versatility, with the Madrid-born youngster able to cover a number of different positions across the midfield and attack.