The Scottish manager is out of contract at the end of the current campaign and has yet to agree a new deal with the club, who lie in fifth place in the Premier League table.
Moyes has been in charge of Everton since 2002 but has never tasted victory at Anfield in a Merseyside derby, with the Toffees’ last away win coming in 1999.
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“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 are go into the match off the back of a 1-0 win over Fulham last weekend and Jagielka hopes that his side’s resolute back line can help the Toffees pick up another win and secure European football.
He continued: “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.”