The Hammers are desperate for more quality in midfield with Moyes keen on players who can help the East Londoners 'look after the ball and pass it better'.
The ambitious move for Davies, who has slipped down the pecking order at Goodison Park under Sam Allardyce, ticks both boxes and would be an exciting coup.
As a player Davies is a real throwback and for West Ham he could be in more ways than one.
The similarities between Davies and Hammers legend Ian Bishop as footballers are striking.
Both elegant and graceful midfielders playing in the same position, the snug-fitting shorts, low socks, long locks, alice band... the lot.
Throw in the fact that, like Bishop, Davies started his career at Everton and the potential that the former could follow the latter from Merseyside to East London is somewhat remarkable.
Ian Bishop in action for West Ham back in 1996
Bishop found his way to West Ham fame via Carlisle, Bournemouth and Manchester City after leaving the Toffees before going on to secure cult hero status with 255 appearances in nine years, scoring 12 goals along the way.
With Allardyce opting for experience as he so often does it could be that West Ham are able to strike a deal for one of the hottest prospects in the English game.
Davies would complement the likes of Mark Noble perfectly in the heart of the West Ham midfield and add some much needed creativity and passing prowess.
Have something to tell us about this article?