The 26-year-old has handed in a transfer request on Thursday, while stating his frustration with life at Upton Park.
Allardyce said that he is yet to receive a bid for the Portuguese forward, but expects an approach before the close of the transfer window on September 3.
"Generally when you [receive a transfer request], they've been tapped up," Allardyce told reporters.
"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."
Vaz Te joined West Ham from Barnsley in January 2012.