Vaz Te, out of favour at Upton Park this season, has asked to leave the Hammers and Allardyce believes that the timing - just a few days before the end of the transfer window - points to an illegal approach.
And Allardyce says he will allow Vaz Te to leave, provided the price is right.
"If anybody's going to leave now it'll be Vaz," he said. "You don't keep anybody that doesn't want to stay. If a club comes in to make the right offer for him we'll be more than happy to accommodate the transfer request he's given us.
"Generally when you make (a statement) like that, they've been tapped up. Someone would've probably already contacted him.
"I am expecting a bid for him in the next couple of days because you don't do that sort of thing this late in the transfer window.
"I would expect in the next couple of days we will have an inquiry. If not he's put himself in a difficult position having said what he's said if he doesn't have another club lined up."
If Vaz Te does not leave, Allardyce says the former Barnsley star can fight for a first team place.
"Nothing is beyond repair with me," he added. "20 years ago, 18 years ago, he'd probably never kick a ball again. In today's world of football and me being a bit more mature and mellow, I'm always ready to give someone a second chance.
"At this moment in time if he wants to leave he can. There's no problem with that. The club who wants him will have to pay a fair price we consider is right. He won't just leave the club because he wants to."