Musonda is a Belgian under-21 international and is regarded as one of his nation's brightest talents, yet finds his path to first team football blocked at Stamford Bridge.
Footmercato report West Ham are keen on an 18 month loan deal to let the youngster, 19, show what he can do, but face competition from Marseille.
Musonda has won both the FA Youth Cup with Chelsea and the UEFA Youth League over the past two seasons, and needs to play first team football to continue his progression.
Chelsea have the starlet tied down to a contract until 2019, and the Evening Standard report the Blues have resisted advances from Manchester City, Arsenal and Manchester United for his signature, and are to cede to his first team wishes by sanctioning a loan agreement.
West Ham already have one player on loan from Chelsea, the more experienced Victor Moses, who has scored once and provided two assists for the Hammers this season.
He is more of a developed player than Musonda, but the teenager has a huge upside, that over 18 months the club would be shrewd to try and benefit from.
Musonda can play on either wing, doing so for Chelsea's under-21s this season, as well as playing in a central role behind a striker.