The Hammers are enjoying their most encouraging run of the season. After pushing Manchester City closer than most, Moyes' men picked up wins - over Chelsea and Stoke City - either side of their goalless draw with the Gunners at the London Stadium.
They have taken seven points out of a possible nine in their last three games, and that has perhaps left Moyes with something of a dilemma: concentrate on the league and make a number of changes for Tuesday's tie, or look to try to keep the momentum going at the Emirates.
Nicholas expects that the Scotsman will opt for the former, and suggested that he is expecting Arsene Wenger's men to book their place in the last four of the competition.
"David Moyes is a friend of mine but it was always going to be a graft for him. The tools were there with the likes of Marko Arnautovic and Winston Reid, who was being touted as a £20m signing for Liverpool 18 months ago, but it has been impressive how quickly he's got them all pulling in the same direction," he told Sky Sports, while explaining why he is expecting Arsenal to win 2-0.
"However, the league has to be the priority here despite climbing a few places and I'd expect seven or eight changes. Arsenal will play some of the kids again but I can see them wearing the visitors down, with the quality of Olivier Giroud and Theo Walcott being enough to get the job done."
With Manchester City seemingly strolling to the Premier League title, the League Cup represents a good chance for Arsenal to get some silverware from the season, so it would certainly be no surprise if they did not make as many changes as the Irons.
But with West Ham high on confidence right now and proving that they can beat the top teams in the division, perhaps there will be some fans who will be extremely disappointed if Moyes makes wholesale changes and essentially rules out their chances of making the semi-final barring a massive upset.
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