The Blue Square South side are the lowest-ranked team left in the competition and held Coca-Cola League One leaders Swansea 1-1 at the weekend.
They are at home to the Welsh side in a replay next week, while Rafael Benitez’s side must overcome Luton to reach the last 32.
Hawks boss Shaun Gale is refusing to get carried away, though, and insists he will not let his attention deviate from plotting a way past Swansea.
“It’s fantastic. We’ve got a tough tie getting past Swansea, I’m sure they’ll want to go there (Anfield) as well,” he reacted.
“Everyone was jumping around, it’s potentially something fantastic for the club, for me and for everyone connected.
“The boys have given me everything.
“They (Swansea) won’t enjoy coming here. It will be a full house and an intimidating atmosphere. We’ve got to make it awkward for them – they are a good side and we’ve got to stop them playing.
“It’s been a fairytale. You see it every season and this year it’s been us and it’s great.”
Club secretary Trevor Brock added: “It’s absolutely unbelievable. What an incentive to get past Swansea. The capacity of our ground is 4,800 and it will sell out without any doubt whatsoever.
“We have been producing miracles all season to get to this stage. We’ll do everything we can against Swansea and what an incentive we’ve got.”
There are two definite all-Premier League ties, with Manchester United at home to Tottenham or Reading, and Wigan at home to FA Cup holders Chelsea.
Newcastle could face league leaders Arsenal twice in four days.
The Magpies, who travel to the Emirates Stadium in the Premier League on Tuesday, January 29, will also run out against the same opposition at the same venue the previous weekend if they manage to see off Stoke in their third-round replay next week.
If West Ham can overcome Manchester City in their replay then it would set up a potentially explosive clash with Sheffield United at Bramall Lane. The Blades still harbour ill feeling towards the Hammers and feel it should have been the west London club who were relegated to the Championship last season for fielding an ineligible player in the shape of Carlos Tevez.
Elsewhere Oldham boss John Sheridan was disappointed to be drawn against Huddersfield and Latics legend Andy Ritchie. Sheridan saw his side produce one of the shocks of the third round as they beat Everton 1-0 at Goodison Park on Saturday.
But any hopes of being pitted against another Premier League giant were extinguished when they were handed a home tie against their League One rivals, who are now managed by Ritchie – a star of Oldham’s run to the semi-finals in 1990.
The Terriers also saw off top-flight opposition in the shape of Birmingham, and Sheridan believes his former Leeds team-mate will be equally disappointed with the draw.
“I’m a good friend of Andy and I’m sure he’ll be disappointed. It’ll be a full house and a game we both think we can win,” he said.
“I heard Andy on the radio this morning saying he didn’t want to draw us. We wanted to avoid each other and go as far as possible. It’s done now and it’s a good game for us. It’ll be a full house, a great atmosphere and a game I think we can win.”