The Daily Mirror reports that United will make the bid for the 21-year-old when the transfer window opens.
Moyes has made two personal checks on the youngster and is ready to makea massive bid to land the midfielder on January 1.
Koke has impressed for Atletico this season and was a key player for the Spain side that won the European U21 Championships last summer.
Bayern Munich, Arsenal and Liverpool are also reportedly interested in the youngster.
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Summer 2016 is set to be a very exciting time for football fans, as this is when the long awaited Euro 2016 tournament kicks off.
Since Guus Hiddink arrived at the helm, Chelsea have improved considerably after a tricky start to the campaign.