The Toffees sit just four points off the third-placed Gunners after a fine run of four wins from their last five Premier League fixtures.
But Everton have also never beaten Chelsea or Liverpool away under Moyes and their last win away to Arsenal came way back in 1996 - but the Scot is hoping to end that run on Tuesday night.
|8/1||Everton are 8/1 to finish in the top four with Paddy Power
Meanwhile, defender Phil Jagielka accepts the criticism thrown at Everton for their poor away record against the league's top sides - but insists all is not lost if they fail to win at the Emirates Stadium.
"You couldn't argue against that and say they are wrong because unfortunately we haven't turned up in some really big games," he told reporters.
"That's the challenge now. There is only one way to change that. But if we don't come away from Arsenal with a win we still can't regard it as a negative. We are going to keep kicking on and kicking on."
Jagielka highlighted Everton's FA Cup quarter-final loss at home to Wigan as a possible turning point in their season.
"I watched the Wigan game [while injured] and the boys were not horrific, but for five minutes of the game we were absolutely blown away. Then we couldn't find a goal that would have got us back in it. You have these sorts of games unfortunately.
"It has happened in a few of our bigger games in the last couple of years and we would like nothing better than to lay that to rest at the Emirates. But it is not always as easy as that."