The Hammers and the Reds enter Sunday's contest against each other at Anfield after winning their opening Europa League group-stage matches by 3-1 scorelines on Thursday, with the former beating Backa Topola and the latter coming out on top against LASK Linz.
The two teams have also made impressive starts to the new Premier League season, although West Ham's unbeaten start was brought to an end by reigning champions Manchester City last weekend.
Indeed, after picking up 10 points from their opening four league fixtures, the Hammers were beaten 3-1 by the Citizens on home soil despite heading into half time with a slender lead.
Liverpool, meanwhile, have won four and drawn one of their first five top-flight matches this season, with a 1-1 draw with Chelsea on the opening weekend followed by victories against Bournemouth, Newcastle United, Aston Villa and Wolverhampton Wanderers.
Including results from the end of last season, Jurgen Klopp's side boast a 16-game unbeaten run in the Premier League, the longest ongoing unbeaten run in the top-flight; the Reds last lost a league game in April by a 4-1 scoreline away against Man City.
Following a busy summer transfer window, Liverpool are seeking to make vast improvements on their efforts in the 2022-23 campaign in which they finished fifth in the Premier League and failed to win a single trophy in all competitions.
Liverpool, who won their solitary Premier League title in 2019-20, are tasked with knocking perennial winners Man City off their perch at the top-flight summit this term, and Moyes believes the Reds have a squad capable of challenging the Citizens for this season's title.
Discussing Liverpool at a press conference on Friday ahead of West Ham's trip to Anfield, Moyes said: "They can challenge for the title. People say we've made a good start to the season but Liverpool definitely have as well.
"They've won (almost) all their games and they're introducing new players into their squad. From a distance, they look like they're getting back into their best form."
The former Everton boss added: "I finished above Liverpool a couple of time as Everton manager and got a few good draws too.
"Finishing above Liverpool has never been an easy thing because of the level, but I hope I can try and do it this year."
Moyes is expecting a difficult test for his Hammers side against Liverpool, adding: "Some teams have got ahead of Liverpool, but Liverpool have pegged them back. It's a big, hard game. The crowd and the stadium play a big role at Anfield.
"In recent years we've given them tough games and we'll try to give them a good game on Sunday. We know we're playing a good side and we want to show what we can do."
It is fair to say that West Ham have struggled when facing Liverpool at Anfield over the years, as they have won just one of their last 50 league matches on the red side of Merseyside - a 3-1 victory in August 2015 under Slaven Bilic - while Moyes have failed to win at Anfield as a manager in 19 previous attempts.
West Ham as sweating over the fitness of star attacker Jarrod Bowen, who is doubtful due to illness, while Aaron Cresswell could also miss out after coming off at half time in Thursday's Europa League win with a hamstring injury.