The Hammers are battling relegation, along with Fulham, and contract talks with the England under-21 international have stalled leaving the door open to a move away from Upton Park.
Morrison was an unused sub away at Manchester City in their Capital One Cup demolition in midweek and mysteriously pulled out of the squad to face Cardiff yesterday, with West Ham picking up a vital three points.
The 20 year old has not been offered an acceptably contract extension and so could leave the East London club for a fee of around £10million.
The Hammers only signed the difficult youngster for £500k, so the owners are contemplating the sale of one of their prized assets despite the club being in massive trouble in the Premier League this season.
Fulham boss Rene Meulensteen worked with Morrison at Manchester United and has made him their number one transfer target this January.