Manchester United look set to mount a serious attempt to strengthen their struggling midfield in January.
The publication also reports that Moyes himself flew out to watch the Spanish starlet in action for the second time last week and that the Manchester United manager has identified the gifted 21-year-old as his primary transfer target.
Koke - full name Jorge Resurrección Merodio - has made quite an impression at the Vicente Calderon in recent seasons.
Under the watchful eye of Argentine Diego Simeone, the young midfielder has taken on much of the creative burden as a talented Atletico side have gone on to pose a real threat to the Barcelona/Real Madrid axis that has dominated La Liga in recent years.
An extra creative dimension in midfield is certainly something that would benefit both Moyes and Manchester United massively.
Since the retirement of the iconic Paul Scholes, the reigning Premier League champions - who currently find themselves in the unfamiliar surrounds of eighth in the top-flight table after a vastly overwhelming start to the 2013/14 campaign - Manchester United have struggled to adequately replace him.
It hardly seems in question that Koke - whose eye-catching displays at club level have seen him force his way into the senior Spanish side - would provide a huge improvement at Old Trafford over the likes of Tom Cleverley and Anderson.
However, what could surely be considered doubtful is Atletico's willingness to see such a talented youngster - not to mention integral figure in their title push - leave the Spanish capital in the near future.