Manager David Moyes was in the Spanish capital last month to run the rule over the player during the Champions League group stage clash against Porto.
"The club have been monitoring his progress for a number of months and scouts have watched him a handful of times," a source told Goal.
Having identified the 21-year-old as a player capable of adding much needed creativity to his side, Moyes, keen to play a far greater role in United’s transfer dealings this winter, has dispatched three of the club's transfer brokers to Spain with a view to securing the latest gem off the Spanish production line.
Having tried and failed to sign three high-profile targets in the summer - Ander Herrera, Cesc Fabregas and Thiago Alacantara - the Premier League champions are especially keen to avoid a repeat, but coaxing Koke from Vicente Calderon will prove no easy task.
Koke, who only in September expressed his delight at having committed his future to the club until 2018, harbours doubts about leaving a club so well placed in La Liga and the Champions League for one fighting to qualify for the same competition next year.
"I am happy to give more years to Atletico," Koke said back in September. "I am at the team of my life and I cannot ask for more.
"I want to continue working to try bring new success and better achievements than last year. I am very happy."
United, meanwhile, are unwilling to pay a large transfer fee, mindful of the fact they have already been quoted €30 million for long-term target Leighton Baines.
The Old Trafford club have also expressed an interest in Inter's Colombian midfielder Fredy Guarin, but the player is understood to prefer a move to Chelsea.
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