"If someone's interested they'll call the board of the club and they'll speak about it but we want to keep him".
The Toffees now sit seventh in the Premier League table, three points behind United and level with Arsenal but having played two games more than both of their closest rivals.
Ronald Koeman's men, who beat the Hammers 2-0 back in October, are now seventh on 57 points - three points behind fifth-placed Manchester United.
"We will wait because it is not the first time he is out".
Andy Carroll and Sam Byram are the latest additions to West Ham's absentee list.
One piece of good news will be the return of centre-back Winston Reid as the Hammers try to work out a way to stop Romelu Lukaku from making it 10 goals in 10 games against West Ham.
"I've got Scott Dann, James Tomkins, Mamadou Sakho, Damien Delaney and Martin Kelly, so actually in central defence we're looking pretty secure", Allardyce said.
And Bilic ruled out striker Andy Carroll, who returned to the starting lineup at Sunderland, after a recurrence of a thigh problem.
Everton's on-loan striker Enner Valencia is ineligible to face his parent club West Ham.
"We have five games left and there are 15 points available". However, they are without a home win since beating Crystal Palace 3-0 in January.
"I certainly think Everton are geared up for success". The Hammers will be using the last few games of the season to jump up as many places as possible in the hope of breaking into the top half of the table.
If Everton are to make up the difference between now and the end of the campaign then they will need to improve their form away from home, where they have won just two of their last 14 league outings.
It's hard not to feel some sympathy for the former Everton defender given numerous problems suffered by the club this season have been out of his hands. There are so many things going against West Ham, it's hard to sum them up in a 15 minute video.
It remains to be seen whether Bilic can inspire his team to finish the season on a high in order to convince the board that he is the right man to take West Ham forward.