Sunday's London derby at Upton Park will pit QPR boss Redknapp and defender Rio Ferdinand against their former club, with the latter in line to make his 500th Premier League appearance versus the team with whom he made his first.
Both sides have made underwhelming starts to the Premier League campaign, West Ham taking seven points from their first six games and QPR are three points worse off in what has been a dismal return to the English top flight so far.
Despite struggling for wins, Allardyce has been pleased with the manner in which West Ham have played to date.
However, the former Newcastle United and Bolton Wanderers boss believes the side's failure to pick up points has placed extra pressure on this weekend's encounter.
"We're under pressure to get more points on the board," Allardyce said.
"We've played very, very well in five out of our six league games so far.
"The fact of the matter is seven points from those games is simply not enough.
"We have to turn performances in to results. I think we should have gained a minimum of 10 or 11 points by now. Unfortunately, we only have seven.
"At this early stage of the season you can jump places very quickly. The QPR game is almost a six pointer. We want to go into the international break with a positive result."
West Ham have not been helped by injuries to a number of key players, with Mark Noble (calf), Cheikhou Kouyate (groin), Joey O'Brien (knee) and Andy Carroll (ankle) all still unavailable.
Defender Guy Demel is also a doubt after picking up a knock in training, but winger Matt Jarvis is close to making a comeback from a thigh complaint.
For QPR, midfielder Sandro could miss out after picking up a head injury in last Saturday's 2-1 loss at Southampton, while Joey Barton and Jordon Mutch are still fitness doubts due to hamstring issues.
Redknapp, who is hopeful that winger Adel Taarabt (ankle) will soon be able to return to training, has earmarked QPR's injuries in midfield as a key reason for their struggles.
"We have been a little too open and teams are getting at our back four too easily," Redknapp said.
"We need to tighten up but it's been difficult because I have brought midfield players into the club and they have never been fit to play together at one time."
But, while Redknapp has had little to celebrate this term, he is relishing an Upton Park return.
"I get to go see a few old friends, there are some great people there and I always look forward to seeing them," he added.
"It's a fantastic club. I went there when I was 15 so I have a lot of memories there, it's a special club to me."
