Arsenal will begin their Carabao Cup campaign with a trip to League One side Port Vale, while Liverpool have been drawn at home against Southampton in the third round of the competition.
The draw, conducted on Wednesday night shortly after Grimsby Town’s shock elimination of Manchester United, marked the entry of clubs competing in Europe this season.
Elsewhere, Chelsea face another away day as they head to Lincoln City, and reigning champions Manchester City travel to Huddersfield Town. Tottenham Hotspur will host Doncaster Rovers, while Newcastle United take on Bradford City.
The third-round fixtures are scheduled to be played in the weeks commencing September 15 and 22.
Full Carabao Cup Third Round Draw:
Port Vale vs Arsenal
Swansea City vs Nottingham Forest
Lincoln City vs Chelsea
Tottenham Hotspur vs Doncaster Rovers
Brentford vs Aston Villa
Huddersfield Town vs Manchester City
Liverpool vs Southampton
Newcastle United vs Bradford City
Sheffield Wednesday vs Grimsby Town
Wolverhampton Wanderers vs Everton
Crystal Palace vs Millwall
Burnley vs Cardiff City
Wrexham vs Reading
Wigan Athletic vs Wycombe Wanderers
Barnsley vs Brighton & Hove Albion
Fulham vs Cambridge United