Southampton will host League Two Torquay in the Johnstone's Paint Trophy Southern Section West second round.
The Saints were handed a bye in the first round as they look to book their place at Wembley, with the winners earning a potential £500,000 from the competition.
They will face a Gulls side full of confidence after an impressive 3-1 win at Cheltenham in round one, with the tie to be played the week commencing October 5.
Norwich have been drawn away to League One rivals Gillingham in the Southern Section East.
A goal from Chris Martin - who helped Luton win the competition last season - was enough for Norwich to beat Brentford at Carrow Road while the Gills were taken to a penalty shoot-out in their first-round tie with Colchester.
League One leaders Charlton have been drawn at home to League Two leaders Barnet after being handed a first-round bye, while the Bees knocked out Millwall, another League One side, with a 2-0 victory at Underhill.
Fellow high flyers Leeds have been drawn at home to Darlington in the Northern Section after Simon Grayson's men were handed a bye in the first round of the competition, while the Quakers snatched a 1-0 win at home to Lincoln.
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