Kane has been in sparkling form for Mauricio Pochettino's side this season and has scored a total of 23 goals during the campaign so far.
Allardyce told reporters at his press conference this morning he plans to stop him from finding the net by stopping the supply lines to him.
He said: "We are aware of his capabilities. He was a surprise at the start of the season and no one expected him to make such an impact.
"But now everyone knows what to expect, the fact he's managed to keep on scoring shows you how good he really is."
It is certainly high praise for the 21-year-old but he isn't the only threat that Spurs have with Christian Eriksen also providing a threat, along with Andros Townsend and Erik Lamela. The latter two probably haven't found the net as much as they'd like but it sounds like West Ham will target that trio to stop any support of supply line.
In his column in the London Evening Standard, Allardyce said: "His rise to prominence has been spectacular and it shows you that, in this game, you never can tell. His previous education, though, when he went out on loan a number of times, has helped him no end and paid handsome dividends.
"Full marks to him, though, and it’s great for England. He looks as though he might be an even more clinical and natural finisher than Wayne Rooney."
Given that the current Manchester United and England captain is on course to break the goalscoring record for both club and country, the praise heaped upon Kane from the manager in the opposition dugout this weekend is incredible.
Rooney himself has something of a habit of finding the net against sides managed by Allardyce, one wonders if it will be the same for Kane?