The Portuguese forward has scored 15 goals in 47 appearances for the Hammers, including the goal that secured promotion back to the Premier League in the 2012 play-off final against Blackpool.
However, he is unlikely to be first-choice this season following the permanent signing of Andy Carroll while other strikers continue to be linked with a move to Upton Park.
Allardyce has already stated that any incomings before the transfer deadline will have to be funded by departures; sparking rumours Vaz Te could be sold to raise funds.
Newly promoted Cardiff were rumoured to have made an approach for the former Bolton forward but when quizzed about those reports Allardyce was quick to play them down, saying agents were probably the source of the story.
“There’s no official bid from Cardiff for Ricardo Vaz Te,” said the 58-year-old. “It always happens at this time of year – it’s just agents getting busy.”
Pedro stepped off the bench to send Chelsea into the FA Cup semi-finals after they beat Leicester 2-1 at the King Power Stadium on Sunday evening.
RB Leipzig came from behind at the Red Bull Arena to end a run of four winless games and defeat Bundesliga leaders Bayern Munich 2-1 on Sunday.