Moyes' comments come as his team prepares to face their local rivals at Anfield, a stadium where he has historically had mixed results.
When asked about his team's performance so far this season, Moyes praised the way his squad has gelled with the new arrivals signed in the summer transfer window.
"We've been pleased with the way the team has come together," he said. "We aimed to be near the top of the league at this stage, and we're now in a position to fight for that goal."
Moyes acknowledged that the team didn't sign all the players they wanted in the summer, but emphasized that they made some good signings and have been working hard to build on their progress.
The manager also expressed a desire for the team to challenge the top teams in the league and to enjoy their football more, rather than struggling to stay afloat as in previous years.
Moyes has a long history of facing Liverpool, and he admitted that it's always been a difficult task.
"Any derby in a big city is important to the fans," he said. "I've always found it tough to beat Liverpool, but we'll be looking to find a victory on Saturday."
Moyes also noted that the gap between the two teams is closer than it has been in recent years, citing the signings made by Liverpool's new manager and the improvement in his own team.
He also highlighted the importance of the game for the players, saying that they know it's a big occasion and a chance to see where they stand in the league.
Moyes was also asked about the form of James Garner, who has been playing well this season.
"Jimmy Garner has been playing well and has made an impact," he said. "He's one of the best English midfielders in the league right now."