It believed that Sir Alex Ferguson is willing to let both players leave for a bargain £4 million price and new Hammers boss Glenn Roeder wasted little time in trying to persuade them that their future lay in East London.
However, The Hammers are unlikely to have a clear run at both the former England Under-21 midfielders as Steve McClaren and Walter Smith are both very eager to discuss terms.
New Middlesbrough manager McClaren is thought to be very optimistic that he can talk both players into joining him at The Riverside, and he will be hoping his previous relationship with them at Old Trafford will play a major role.
Everton have denied any interest in the duo, and it seems that will leave West Ham and Boro in the hunt.
Ipswich and Fulham are also said to be monitoring the situation, but it is not yet known whether either will make their interest official.
Town boss George Burley has just missed out on Hassan Kachloul to Aston Villa, and Fulham likewise with Liverpool for Norwegian John Arne Riise and so both could very well be in a position to make a move.
Wilson was offered a new deal last season to stay at Old Trafford, but this was rejected as he realises that he is way down the pecking order and has little hope of breaking into the first team, and for similar reasons Greening (pictured) has decided that his future lies elsewhere.
