Spurs manager Harry Redknapp has never hidden his admiration for Parker, but conceded a deal could be difficult due to the finances involved.
Parker is expected to leave Upton Park this summer as he seeks to stay in the Premier League following West Ham's relegation to the Championship.
However, Allardyce insists if Spurs leave it until the last minute to swoop for Parker they will be left disappointed.
"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."
West Ham expect Parker to move on before the close of the transfer window, but Allardyce claims there are no bids on the table for the England international.
"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," added Allardyce.
"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."