The fact the game has been chosen by the BBC for live primetime coverage on Saturday evening shows they sniff an upset, and with good reason.
The Toffees head east still smarting from that error-strewn 3-2 defeat against Brighton last weekend, meaning it is now just one win in 12 games stretching back to the end of October.
Evertonians are nearly at breaking point, with most of their anger aimed at Rafa Benitez.
The Spaniard is not solely to blame for the club’s problems, but some of his tactics and line-ups are open to question - and how hard is it to set up a team to defend set pieces properly?
Then there is the Lucas Digne saga.
Benitez came out fighting in his news conference on Friday, saying Digne wanted to leave and accused him of being more concerned about his personal stats than the team.
The Toffees boss certainly has form for this, his abrasive management style means he has fallen out with people at nearly every club he’s been at. But given we have not heard from Digne we don’t know the full story and have to trust what Benitez is saying is true.
Inevitably there is little of that around, not just because of his Liverpool connections, but the woeful performances and results we’ve had to endure over the past few months.
All that fallout has overshadowed what has been a successful transfer window for Everton so far, with Nathan Patterson becoming the second new arrival of the window and finally ending their long search for a right back.
At just 20 he is very much one for the future, but there’s no reason why he can’t share full-back duties with Seamus Coleman between now and the end of the season.
With Vitaly Mykolenko also on board and more new faces expected there are some reasons to be optimistic.
But some positive results are needed quickly to ward off the sense of crisis currently surrounding the club.
It’s nearly five years since Everton met Hull, with the Tigers’ relegation at the end of the 2016-17 campaign (under Marco Silva no less) signalling the start of several seasons of toil.
Like many teams who drop out of the top flight Hull struggled to bounce back, finishing 13th and 18th before eventually finishing rock bottom in 2019-20 to drop to the third tier for the first time since 2005.
The board kept faith with Grant McCann and were rewarded with an immediate return to the Championship as League One champions.
Like Everton, Hull currently find themselves too close to the bottom three for comfort, with just four points separating the Tigers in 19th and the final relegation place.
Also like the Toffees, they are likely to go into the game slightly undercooked having played just once in the last three weeks because of Covid cancellations.
They do have recent history in the competition, reaching the final in 2014 and taking a 2-0 lead against Arsenal before eventually losing 3-2 after extra-time at Wembley.
Everton will be without Dominic Calvert-Lewin, with the Toffees saying the striker is being eased back into action following his length layoff (though rumours earlier this week suggested he had felt his thigh muscle following the Brighton game).
That will likely mean the much-maligned Salomon Rondon will be handed a start, though youngsters Ellis Simms and Lewis Dobbin could also come into contention.
Andros Townsend is back in training after a broken foot but is unlikely to be risked. Tom Davies, Richarlison and Yerry Mina are all still sidelined.
Benitez says he will assess new signings Vitaly Mykolenko and Nathan Patterson before deciding whether to hand them their debuts.
Dominic Calvert-Lewin scored his first Everton goal as the Toffees eased to a 4-0 win over Hull the last time the two sides met in March 2017. Enner Valencia and a double from Romelu Lukaku completed the win.
What they said
Everton boss Rafa Benitez: “Every game is massive and I know how important the Cup is for the club and our fans.
“If we can do well in some games, we’ll have more confidence and it will be easier to approach the next games.
“We have experience of what it means for [lower league] teams to play against Premier League sides. It will be tough, for sure, but we are ready.
“I was pleased with the training session yesterday.
“The players were pushing and working hard. They realise after the Brighton game we have to perform and do well. Mentally, we are ready.”
Hull boss Grant McCann: “We see it as an opportunity to try and get through to the next round.
“We understand that they are littered with quality all the way through their team but we’re at home and expecting a big following. We want to go and give it a go and see if we can get ourselves into the next round.
“They haven’t won as many games as they would’ve wanted, but over the last eight or nine games they’ve beaten Arsenal and drawn with Chelsea and Tottenham, so they’re a good team.
“It’s just not going their way at this moment in time. Whichever 11 players they put onto the pitch, they’re going to be internationals and top-class players. We want to try and keep the focus on ourselves.”
Let’s face it, this has got cup shock written all over it. And the way Everton are playing at the moment gives me little faith that they will prove me wrong.