Liverpool, eight-time winners of the competition - most recently in 2012, are not in Europe this season so enter at this stage and were arguably the plum draw in round two. Leacock certainly thinks so.
While the centre-half acknowledges they are firm underdogs, he points to Bradford's exploits last season. The west Yorkshire club became the first team from the fourth tier for half a century to reach the final, claiming the scalps of Premier League trio Wigan, Arsenal and Aston Villa en route to Wembley.
Leacock believes this should inspire him and his team-mates.
The 29-year-old said: "It is a dream draw for us. As soon as we beat Fleetwood in round one we all wanted a big draw and we have certainly got it. It is the biggest draw we could have got - it is brilliant for the players, the fans and the club as a whole.
"Liverpool are one of the biggest clubs in the world so it is going to be very special to play at Anfield - and anything is possible.
"Of course, everyone will be expecting us to lose. But we can go there without any fear, without any pressure, and you never know what could happen. Look at Bradford last season. They beat Arsenal and Aston Villa and made it all the way to the final so anything can happen.
"Sometimes the big clubs don't play their big-name players. I don't think they will have Luis Suarez available, so that is a huge relief personally as he is one of the best strikers in the world. I am glad I won't be coming up against him.
"We know we will need a lot of things to go our way, a little bit of luck on the night, but I am sure we will sell-out our tickets and pack the away end and us players will give it everything we have got."
History is not on Notts County's side, though. They have conceded 14 goals in their last three visits to Anfield and last won on the red half of Merseyside in 1902.
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