The young Foxes booked their spot in the last 16 after at King Power Stadium on Monday 19 January, having already by the same scoreline in the previous round.
Southampton, meanwhile, advanced to the fifth round after beating Everton at Goodison Park on penalties after the game finished 1-1 in normal time.
Leicester and Southampton have already crossed paths in the Barclays U18 Premier League this season when they met at Belvoir Drive in late November, with the match finishing 1-0 to the visitors on that occasion.
Tickets for the game at St. Mary's Stadium are priced at £3 for Adults and £1 for Over-65s and Under-17s. Supporters can purchase tickets at the turnstiles on the night of the match on a cash-only basis.