The West Ham boss believes that his side must lose no more than 10 games to qualify for Europe.
The Hammers are flying high this term, sitting in fifth place following their 2-1 victory over West Brom on Tuesday evening.
Having overcome a host of injuries to lead his side into the upper reaches of the Premier League table, Sam Allardyce has been praised for his management of the club, especially for his decision to emphasise a more attacking style of play at the Boleyn Ground.
A number of impressive summer acquisitions have aided the East London club on their task, and the pressure that was on Allardyce's head at the opening of the campaign has all but disappeared.
Of 14 games played this season, the Irons have won 24 points, with seven wins and four losses an impressive record heading into the festive period. Having already overcome a serious injury problem, fans will be hoping that luck is on their side and they can progress through the intensely scheduled month of December with a string of positive results.
Any potential chance of securing a top five finish - the clubs joint-best since the Premier League began in 1992 - will rely on enjoying a good Christmas period, and Allardyce believes that the 27 points available between now and the end of January will play a 'massive role' in the Hammers fortunes this season.
Speaking to the Standard, the 60-year-old coach said: "Between now and the end of January we have nine Premier League matches, not to mention rounds three and four of the FA Cup.
"With 27 points up for grabs, that will have a massive effect on where we finish in the table."
Allardyce also outlined the Hammers chances of qualifying for Europe rely on suffering no more than 10 defeats over the whole season - with four already registered this term.
"Can we qualify for Europe?" he added.
"If we carry on as we have, that is not an unrealistic ambition. However, we are only just over a third of the way through the season and many things can happen. It’s right for the fans to have their dreams, though, and it’s our job to try and make those dreams a reality.
"We’ve lost four games this season and if we want to finish right up there, we can afford only eight defeats or maybe 10 at most.
"That’s difficult for any team but certainly it looks as though we might be able to achieve it."