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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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.