Both sides have suffered back-to-back defeats under their new managers and are in desperate need of a confidence-boosting result on Saturday afternoon.
The general impression you get from Unai Emery, despite his side beginning the season with losses to Manchester City and Chelsea, is that there are plenty of positives to take into the remaining nine months of the season.
Emery was fully aware of the magnitude of the task facing him when agreeing to take over from long-serving boss Arsene Wenger at the Emirates Stadium, and so it has proved with defeats to the reigning champions and the side they dethroned at the top of the pile.
Some have suggested that Arsenal look no different to the final few years under Wenger, with their defensive frailties costing them in the big moments, while others - namely Ray Parlour and Gary Neville - have sided with Emery and backed the Spaniard to get things right over time.
The former Sevilla and Paris Saint-Germain chief has a proven track record for success, and already he has shown that - unlike Wenger - he is willing to make some big calls. Mesut Ozil, for example, was subbed against Chelsea; contract rebel Aaron Ramsey was left out of the starting lineup entirely for that early-season showdown.
The tough run of fixtures to start this new tenure has to be factored in, then, but ultimately Emery has to live with the fact that he is the first Arsenal boss to lose his first two matches since Steve Burtenshaw in 1986.
Defeat this weekend, meanwhile, will make it just the fifth time in the Gunners' illustrious history that they have started a season with three successive defeats - the last of those coming in 1954-55.
For all their problems during Wenger's final term, Arsenal did hold claim to a very impressive home record which was bettered only by champions Man City - 47 points from a possible 57 and just two defeats in the red half of North London all campaign.
Now it is a case of the Gunners taking the few positives from their opening-game defeats and putting it to good use this weekend. Victory over West Ham and all of a sudden the mood is a lot more positive; defeat, though and already the pressure will begin to mount on Emery.
Recent form in Premier League: LL
Recent form (including pre-season): LWDWLL
West Ham United
On the back of a summer that saw West Ham pull off a coup of sorts by landing Manuel Pellegrini, making him the third-best paid boss in the Premier League in the process, and splashing out £100m on new recruits, starting the season with successive defeats is not ideal to say the least.
The 4-0 defeat to Liverpool on the opening weekend was followed up by an even more disappointing 2-1 home loss to Bournemouth, with the Hammers surrendering a one-goal lead to the top flight's comeback kings last week.
Already players are pleading for patience, with goalkeeper Lukasz Fabianski - one of the nine new recruits being integrated into the side - insisting that it was always going to take time for him and his new teammates to click together.
Pellegrini, meanwhile, believes that United are suffering a hangover from last season's disappointing campaign, and the title-winning boss even suggested that his players 'lacked trust' in their defeat to Bournemouth at the London Stadium.
Hardly a ringing endorsement, then, and should two defeats become three on Saturday, it is fair to say that the bubble will have well and truly burst.
An aggregate 6-1 scoreline points to a side that cannot defend and struggles to score, yet all this could well have been resolved by bringing in a standout name in defensive midfield. Pellegrini's job is to make his side more solid in the middle of the park, which in turn should make the Hammers stable at the back and more efficient in attack.
This is hardly the best of fixtures for Pellegrini to prepare for following a difficult first couple of weeks, but West Ham have - in context - a positive overall record away at Arsenal in the Premier League, winning three times at Highbury and twice at the Emirates Stadium.
Only Liverpool (7) and Manchester United (8) have a better record, in fact, so this could well be the weekend that the East Londoners get their latest new era up and running.
Recent form in Premier League: LL
Recent form (including pre-season): WWDWLL
Guendouzi's place looks safe, having produced a combined 17 tackles and interceptions already this term - four more than any other player in the division - and enjoyed more touches of the ball (139) than any of his teammates.
Emery may be tempted to work Ramsey back into his starting lineup, which could be bad news for misfiring Ozil, while Alexandre Lacazette will feel that he is worthy of a first start in one of the wide attacking positions.
As far as the visitors are concerned, all eyes will be on Jack Wilshere following his Emirates Stadium exit in the summer. The English midfielder made 197 first-team appearances for Arsenal and was part of the 2014 and 2015 FA Cup-winning sides, but he is eager to "prove a point" this weekend.
Free signing Ryan Fredericks has already lost his place in the side, meanwhile, with Arthur Masuaku and Pablo Zabaleta being preferred at full-back, and in attack there could be a quickfire return to Arsenal for Lucas Perez after being eased back to full fitness by Pellegrini.
Arsenal possible starting lineup:
Cech; Monreal, Sokratis, Mustafi, Bellerin; Guendouzi, Torreira; Iwobi, Ramsey, Mkhitaryan; Aubameyang
West Ham United possible starting lineup:
Fabianski; Zabaleta, Balbuena, Ogbonna, Masuaku; Noble, Sanchez; Perez, Wilshere, Anderson; Arnautovic
Head To Head
Arsenal beat West Ham 4-1 at the Emirates Stadium in April to begin Wenger's month-long farewell in style, earning the points through a burst of goals late in the match.
That made it six without defeat against the Hammers in all competitions, while going further back they have lost just one of their last 22 overall - a 2-0 setback on the opening day of the 2015-16 campaign.
The Gunners, unbeaten in their last nine home London derbies, have won 28 of their 44 top-flight encounters with United.
We say: Arsenal 2-0 West Ham United
Arsenal and West Ham are in desperate need of lift-off after making losing starts to life under Emery and Pellegrini respectively. The Gunners played some good football at times at Stamford Bridge last time out and should, judging by the Hammers' opening two games, finally get off the mark this weekend in a fixture that they tend to do well in.