The Red Devils are known to be in the market for midfield reinforcements, having spent much of the summer looking to bolster their creative ranks.
Koke fits the profile they are after, with the 21-year-old having both age and ability on his side.
He has shone on a regular basis for Atletico since breaking into their first-team ranks and has earned senior international recognition with Spain.
Koke played the full 90 minutes in midweek as Atletico eased their way through their final group stage fixture in the UEFA Champions League.
The youngster is, however, adamant that he is unaware of any imminent approach from England and claims to be happy where he is - having only recently committed himself to a new contract which is due to run until 2018.
Koke told Canal Plus on the United reports: "I didn't know anything (about Moyes watching on), but I'm not concerned (with any of that). I renewed in the summer."
Atletico were happy to accommodate Moyes and he held talks with the club's sporting director Jose Luis Caminero.
He claims that no transfer discussions were held, with little indication offered from the United camp that they were there to cast an eye over potential targets - with in-form frontman Diego Costa also said to be in the thoughts of the Premier League champions.
Caminero said: "I suppose he came to see us because Atletico are a Champions League team and because they also qualified for the last 16.
"We spoke, but he didn't tell me exactly why he had come."
@jelasfirsttouch (Everton)> You do know he plays for Athletico right? Even their coach doesn't believe they can win the league. "Diego Simeone said he is convinced La Liga is still boring". He goes further to state, that his team won't win the league. So your the only one who believes they can win the league or CL. Even the coach is realistic enough to know, they won't win.- Synergy
So Koke could follow the lead of David Silva, Torres, Mata etc and come to a league and play for a team that should consistently be capable of challenging for trophies in United, rather than stay at Spain at a club that has no chance at trophies and will lose essential players every year coz of the uneven distribution of cash in the La Liga.