Last month, the Reds were drawn into Group A of the Northern Section and will play one match each against Aston Villa, Durham, Everton and Sheffield United.
Ahead of the competition’s start, and the new season which gets under way this weekend, the dates and times of those fixtures have now been confirmed.
United’s League Cup campaign will begin with a trip to face Aston Villa, with a 12:30 BST kick-off at the Poundland Bescot Stadium on Saturday 1 October.
A return to Durham’s Maiden Castle, having played there in last season’s competition, then follows on matchday two.