The England international is expected to leave Upton Park following the East Londoners' relegation from the Premier League in May, but as of yet there have been no bids deemed acceptable by the club's owners.
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Spurs are one of a host of sides said to be keen on signing the Hammers skipper. Reports back in May suggested North London rivals Arsenal were also interested in a deal for the 30-year-old, with a view to adding some steel to their midfield.
And Allardyce is concerned that Harry Redknapp's side may be waiting until the dying embers of the window in the hope of forcing down West Ham's asking price.
“It is a worry that Spurs might wait until the last minute because it would be the wrong time to do it,” said Allardyce.
“If they want to come and do it, then I will be telling the chairmen it is the most expensive time and not the cheapest.
“So if Harry is listening, or anyone at Tottenham, watch out, don’t be waiting that long because you won’t be able to do it.
“There are no bids for Scott at the moment so we continue to improve him as if he is going to start the season in our team, until such time as somebody bids the right money that would be acceptable to the club,” the Hammers' boss explained.
Parker is one of a host of big name players who had been expected to leave West Ham this summer, but are still to depart.
There has been widespread speculation regarding the futures of Robert Green and Carlton Cole, but the pair have also yet to leave the club, a situation that Allardyce admits is difficult.
“It’s like that for every player at ever club. There is speculation and that will continue right through to August 31 unfortunately, but that is the way it is.
“We need to deal with it, it is very, very difficult indeed, but there is not a lot we can do about it.”
West Ham are set to start their Championship campaign in less than a fortnight, with a home clash with Cardiff City on August 7.
