It will be the second meeting between the two teams in the space of a week, with the pair playing out a goalless draw in the Premier League at the London Stadium on December 13.
The result saw the Gunners end a run of three Premier League games without a win, but an inconsistent 2017-18 campaign to date has left Arsene Wenger's side in fifth position in the table after 18 matches.
With Arsenal having their problems in the Premier League in recent weeks, the EFL Cup might well prove to be a welcome distraction. West Ham are the visitors to the Emirates Stadium, and a win over their London rivals would book their spot in the semi-finals, which will take place next month ahead of a February final.
Arsenal have beaten Doncaster Rovers and Norwich City to book their spot in the quarter-finals of the EFL Cup, but they have only actually won this particular cup competition on two previous occasions – 1987 and 1993.
It might well be the club's best chance of silverware this season, although Wenger will fancy his chances of challenging for the Europa League title and leading another successful FA Cup campaign.
Arsenal have a massive Premier League game against Liverpool in London to come on Friday night, but that is for then and this is for now as the Gunners look to continue their journey in the EFL Cup.
Recent form: WW
Recent form (all competitions): WLWDDW
When West Ham lost 4-0 at Everton on November 29, it would be fair to say that the club's supporters could not have been more pessimistic. David Moyes was struggling in his new position, and there was a genuine fear that the Hammers could be relegated from the Premier League this season.
West Ham were much improved in their 2-1 defeat at Manchester City at the start of December, however, before taking four points from home Premier League matches against Chelsea and Arsenal.
Moyes then led his team to a 3-0 victory away to Stoke City on Saturday afternoon, which propelled the Hammers up the table. There is suddenly a serious confidence about this West Ham outfit, and they will be confident of getting a result at the Emirates Stadium after holding Arsenal last week.
Unlike Arsenal, West Ham have had to win three matches to reach this stage of this season's EFL Cup. Indeed, they overcame Cheltenham Town back in August, before beating Bolton Wanderers and Tottenham Hotspur to advance.
The Hammers have never actually won this particular competition, but they are within touching distance of the semi-finals, and there is every reason to suggest that they could cause Arsenal some problems on Tuesday night.
Both managers will make changes for this match ahead of what is a busy festive period in the Premier League, but the opportunity to make the semi-finals of a major cup competition does not come around for West Ham every day.
Recent form: WWW
Recent form (all competitions): DLLWDW
Theo Walcott cannot buy a minute of Premier League action at the moment, but the England international is expected to start in a much-changed Arsenal team.
Declan Rice, Javier Hernandez, Andre Ayew and Diafra Sakho are also pushing for places in the XI as Moyes is sure to rotate, but the West Ham boss should still send out a team full of experience as he looks for yet another positive result.
Arsenal possible starting lineup:
Ospina; Maitland-Niles, Holding, Chambers, Debuchy; Wilshere, Coquelin, Elneny; Walcott, Giroud, Welbeck
West Ham possible starting lineup:
Hart; Rice, Reid, Ogbonna; Fernandes, Noble, Obiang, Cresswell; Ayew, Hernandez, Lanzini
Head To Head
As mentioned, the two teams played out a goalless draw when they met at the London Stadium in the Premier League last week.
Arsenal ran out 3-0 winners during their last clash at the Emirates Stadium, however, and the Gunners are unbeaten in their last four with the Hammers.
That said, West Ham have a recent win at the Emirates Stadium to their name – recording a 1-0 victory on the opening weekend of the 2015-16 Premier League campaign. It will be the first time that the London rivals lock horns in a competition other than the Premier League since an FA Cup clash in January 2010.
We say: Arsenal 2-1 West Ham
Both managers will ring the changes following their clashes at the weekend, which should create an open and entertaining affair. West Ham will enter the match full of confidence, but we fancy Arsenal to just shade the contest.