The Reds have won the competition the joint-most times, with eight and level with Man City, but last lifted the trophy back in 2012.
A run to the final was last seen in 2015/16 in what was Jurgen Klopp‘s first season at the club, but since then a semi-final berth is as far as the club have progressed.
Last season, Liverpool played out a 0-0 draw with Arsenal in the fourth round before being knocked out in a penalty shootout after easily putting Lincoln City to the sword by the tune of 7-2.
And now Norwich at Carrow Road awaits in the third round this season, which is to be played out in the week commencing September 20.
It will, of course, be the second time the two sides have met this season after the Reds dispatched the Canaries 3-0 on the opening day, but it is only the third time the two clubs have met in this competition.
The last time was in 1982/83, where Liverpool went on to win the trophy.