Allardyce told reporters Vaz Te had handed in a transfer request and West Ham would be "more than happy" to accommodate it if a club came in with the right offer before Monday's transfer deadline.
"He might leave now, if anybody's going to leave now it would be Vaz. You don't keep anybody that doesn't want to stay," the club website (www.whufc.com) quoted Allardyce as saying ahead of West Ham's weekend match at home to Stoke City.
"I would expect that in the next few days that we probably will have an inquiry."
Frenchman Diarra was injured in Wednesday's Capital One (League Cup) second round win over fourth tier Cheltenham Town.
"The injury is more serious than we expected and it's an ACL reconstruction it looks like, so that will almost certainly finish Alou's season," said Allardyce.
"It's a big blow to us in squad terms, he was hoping to force his way into the side this season but obviously after that injury that now won't be the case."
(Reporting by Alan Baldwin, editing by Tom Bartlett)
