The Wales international failed to find the net in Tottenham’s 1-1 draw with Lyon in the Europa League last week, ending a run which saw the midfielder score in four successive games.
The 23-year-old has scored an impressive 13 goals in 23 Premier League goals this season, including a strike in a 3-1 victory over West Ham at White Hart Lane.
And Allardyce believes Bale could be subject to offers from outside of the English top flight in the summer amid reports interest from Spain.
“The world of football outside of this country might decide his worth,” said Allardyce.
“There might be somebody else from another country that decides he could be the man, so that would inflate the price a little more.
“I would have thought that Tottenham would want nothing less than £40-50m.”
Although Allardyce admits Bale is the obvious danger-man on Monday night, the Hammers boss says his side cannot afford to focus all their energy on keeping the winger quiet.
“The main thing for us on Monday night is to worry about ourselves,” he added.
“We understand that Tottenham have got lots of fantastic players and they are a great team – but we’re not bad ourselves.
“Everybody’s talking about Gareth Bale because he’s playing well and scoring goals. He’s one of a number of players that we’re going to try to have to shackle to get a good result.
“We’ve got to keep as close an eye on those players as we can but also go and do our stuff when we get the chance.”
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