Moses has fallen down the pecking order at Chelsea following the addition of Pedro but, according to the Guardian, the Nigerian international will sign a new contract before moving to the Boleyn Ground.
The 24-year-old joined Chelsea from Wigan Athletic in 2012 and has made 44 appearances scoring 10 goals, however he has not made a Premier League appearance for the Blues since 2013.
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He spent the last two seasons away from Stamford Bridge, on loan at Liverpool and Stoke City and will be able to play more first-team football under Slaven Bilic at West Ham.
At 24, Moses still has time to make his career at Chelsea a success and the offer of a new deal shows Jose Mourinho still has high hopes for the winger.
He impressed during pre-season and if the former Crystal Palace man can find his top form while on loan, he could be involved with the first-team in West London next season.
Chelsea have struggled so far this season and Kurt Zouma has declared the players are struggling with being defending champions. Having failed to entice John Stones from Everton, the Blues are now in talks over a deal for Nantes defender Papy Djilobodji.
With Manchester City already eight points ahead of Chelsea heading into the international break, the Blues desperately need to improve their fortunes after the two week break.
A major issue for Mourinho's men at the start of this campaign has been their lack of defensive cover in midfield. They have been linked with Paul Pogba and should be doing their utmost best to complete a deal for the France midfielder before the window closes.