The fee could rise to £1million after Morrison's agent spent the day negotiating personal terms for the 18-year-old.
Hammers boss Sam Allardyce told the London Evening Standard: 'Ravel is a talented lad and if he really wants to be a player then we will help him as much as we can along the way.
'Perhaps a change of environment will be beneficial to him and help him make that step up to first team football quicker than perhaps would have been the case at Manchester United. There is no doubt he has exceptional talent.'
Morrison, whose deal expired at the end of the season, stunned United by demanding a huge new contract despite the player making just three first-team appearances.
Sir Alex Ferguson has expressed his exasperation with the talented but troubled teenager, describing his demands as 'unrealistic'.
West Ham are also poised to sign strikers Nicky Maynard and Ricardo Vaz Te from Bristol City and Barnsley respectively.
Wanted: Nicky Maynard could join Morrison at Upton Park
Wanted: Nicky Maynard could join Morrison at Upton Park
Maynard, who was also out of contract this season, is wrapping up a £2.25m after impressing in the Championship.
Vaz Te, who was signed on a free transfer from Hibernian in the summer, has been a revelation at Oakwell this season, scoring 12 goals in 24 appearances from a wide position.
The Lisbon-born forward penned a one-year deal with the Tykes and was reported to have rejected a new deal earlier this month.
His form and contractual situation has attracted the attention of Allardyce, who brought the 25-year-old to England in 2003 while at Bolton, and Barnsley confirmed that they have given the two parties permission to discuss a deal after an undisclosed fee was agreed.
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