This time, the action will be in the Carabao Cup, which enters its Last 8 stage.
West Ham have been in great form under the management of Moyes.
West Ham have enjoyed a recent upturn in results under new manager David Moyes following two victories and one stalemate.
The Hammers would be confident of a big scalp in this round as well as they come into the game on the back of some fantastic relegation pull-away form.
Bournemouth are finding life hard this season, and were spanked 4-0 by Liverpool last time Sunday, so they will hardly go into this game full of confidence. Ahead of their latest meeting on Tuesday, The Hard Tackle takes a closer look at the encounter.
"There will be some players we do play and some players we don't play, just like every game".
"Shkodran is back again".
Wenger confirmed that Theo Walcott is back from a groin problem and will start against the Hammers at the Emirates.
If previous rounds are any indication, a number of players are set to be rested, including Mesut Ozil, Petr Cech, and Alexis Sanchez.
"David Moyes is a friend of mine but it was always going to be a graft for him".
Jose Fonte, Sam Byram, Cheikhou Kouyate and Edimilson Fernandes are all ruled out through injuries, with Manuel Lanzini facing a charge over diving.
Mark Noble is a doubt after he was withdrawn in the first half due to a hamstring injury.
Winston Reid is available, whilst Andy Carroll could return, however, the West Ham boss has stated that it could be a last-minute decision.
No player has had a hand in more Carabao Cup goals this season than West Ham's Andre Ayew (3 goals, 1 assist).
The League Cup represents a realistic shot at silverware for Wenger and his Gunners squad this term. This will be the 14th quarterfinal tie for the Gunners under the Frenchman. They have 5 more in the next three weeks.
Will he set things right this time around? The two teams met a week ago at the London Stadium in a match that ended in a goalless draw.
So far, Arsenal have managed the period pretty well.
"It's a very exciting bunch of young players", Wenger said. Since then however, they've lost seven of their nine visits to the ground (W1 D1), with an aggregate score of 19-4 to Arsenal.
That could eventually be a factor, which is why The Hard Tackle is going with a narrow 2-1 win for Wenger & co.