The reverse fixture between the sides was marred by anti-semitic abuse aimed at Spurs' supporters and the Hammers manager does not wish to see a repeat on Monday evening
Several incidences of anti-semitic chanting were reported during the reverse fixture at White Hart Lane earlier this season, with Hammers supporters widely condemned in the aftermath.
And Allardyce says the home support must refrain from such abuse when the London rivals do battle at Upton Park.
"I hope there's nothing untoward that happens in terms of chanting,” the Englishman told reporters ahead of the game.
"Like everybody else we want to try to reduce it to its bare minimum. We'd like to cut it out completely but I don't think that's ever going to be the case when people get involved in emotional situations.
"But if we spot it we've got to deal with it and hopefully there won't be any."
There was also a stern warning from West Ham co-chairmen David Gold and David Sullivan, who insisted fans will be severly punished for offensive chanting.
"We must be clear that we will pursue the harshest sanctions against any individual who goes against what we stand for as a club," they said in a joint statement.
Allardyce, meanwhile, went on to pinpoint Gareth Bale as Spurs' biggest threat, with the Welsh winger having scored 17 goals in all competitions this term.
He continued: "Not only has he scored very important goals, but they've been stunning goals at that.”
"He's going to need some looking after on Monday night. If we can do that we nullify a threat that Tottenham have. Of course Aaron Lennon is a threat down the other side, but he doesn't quite score as many goals as Gareth Bale."
The Englishman also lamented the fact that his side face only three fixtures in March, having seen their match against Manchester United postponed due to FA Cup commitments.
"Selection processes are what a manager needs and it gives us a good, broad base of squad members in strength in depth to select from moving forward in the last third of the season," he said.
"Our difficulty is that coming into March we've only got three games in the month. It's going to be a big period to actually manage the players without really enough games.
“We'll keep on top of the players' fitness and make sure we're ready for every game because with such long periods [between games] keeping the players focused and concentrated is one of the difficulties.”