Moyes, who is out of contract at the end of the current campaign and is yet to sign a new deal, has not enjoyed victory away from home in a Merseyside derby, with Everton's last win at Anfield coming in 1999.
"No one knows what the manager is going to do at the end of the season, so if it is going to be his last game as Everton manager at Liverpool then it would be nice to send him off in style," he told the Liverpool Echo.
"But it's not just about him it's about the squad as well, and we'd all love to go there and perform the way we have for most of the season and come out on the right side."
Everton returned to winning ways with a 1-0 victory over Fulham on Saturday, while three points against Liverpool would keep alive their slim hopes of Europa League qualification.
And the England defender believes Everton's stubborn defence gives them every reason to be optimistic heading into the Merseyside derby.
He added: "It's nice to get a few clean sheets on the spin, especially at home. It does ease the nerves a little bit. We were going through a stage where we couldn't buy one so it's nice to grab them now.
"Hopefully we can carry that on throughout the rest of the season and keep pushing as far as possible.
"We played a lot better football probably for the first half of the season. The pitches were a bit better back then."