Fulham host League One AFC Wimbledon at Craven Cottage, in the Carabao Cup second-round draw. It will be the first time the two teams have faced each other.
Chelsea will host Jack Wilshere's Luton Town in the Carabao Cup second round, while Tottenham Hotspur host Charlton Athletic in a London derby.
The 11 Premier League sides not involved in European competition this season joined the winners of the first-round ties in the hat.
Among the other tasty ties are League One AFC Wimbledon visiting Alvaro Arbeloa's Fulham at Craven Cottage, while Keith Andrews' Brentford face a potentially tricky tie against Birmingham at St Andrew's.
The winner of the Devon derby between Plymouth and Exeter, live on Sky Sports on Monday night, will get Premier League side Coventry City at home, while West Ham face an all-Championship tie away to Southampton.
In the north draw, Newcastle have been given Championship side West Brom at home, while Leeds were given an all-Premier League clash against Nottingham Forest. David Moyes' Everton go to second tier club Preston.
Like the first round, the second round draw was also regionalised and split into Southern and Northern section ties. The second-round matches will be played in the week commencing August 24.
The remaining Premier League teams will join in the third round, which will be split over the week commencing September 7 and the week commencing September 14. The teams competing in the Champions League will start in the later week.
South Draw (To be played in the week commencing August 24)
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Fulham vs AFC Wimbledon
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Walsall vs Leyton Orient
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Ipswich vs Leicester
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Cardiff vs Norwich
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Stevenage vs Reading
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Cambridge vs Millwall
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Birmingham City vs Brentford
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Southampton vs West Ham
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Watford vs Peterborough
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Plymouth or Exeter vs Coventry
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Chelsea vs Luton
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Tottenham vs Charlton
North Draw (To be played in the week commencing August 24)
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Stoke City vs Hull City
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Newcastle vs West Brom
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Blackburn vs Sheffield Utd
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Nottingham Forest vs Leeds
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Doncaster vs Middlesbrough
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Barnsley vs Crewe
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Preston vs Everton
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Blackpool vs Lincoln
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Sheffield Wednesday vs Wolves
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Bradford vs Burnley
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Fleetwood vs Shrewsbury