The 28-year-old helped the Championship side eliminate Fulham from the competition two years ago and is hoping to produce another impressive display as PNE target another cup upset.
“It'll be good to go out there and put on a performance. It's nice to progress in the cup and potentially beat a Premier League outfit like Everton,” Storey told the club website.
“We'll be going in confident, knowing how we want to play and looking to tidy up on some of the things we've got wrong in the previous two games.
“We had it with Fulham a few years back where we ended up beating them. We want to try and replicate that again against Everton. They are a really good team and they've got some great players. They'll be wanting to progress and looking to challenge to win the cup this year.
“We know it'll be a tough test. But again, it's going to be a good fixture for us and hopefully we can perform on the night.”