The 26-year-old’s future has been the subject of rife speculation this summer after he began agitating for a move away from Anfield.
Should Suarez stay past next week’s transfer deadline, his first match back after biting Chelsea defender Branislav Ivanovic last season will be at Old Trafford against United.
Wigan shocked Manchester City to triumph in the FA Cup last May and they travel to the Etihad Stadium.
Jose Mourinho’s first taste of the competition he twice won in his previous spell as Chelsea boss will be at League One outfit Swindon.
Holders Swansea kick-off their defence at Birmingham. There are a number of all Premier League ties. Arsenal are at West Brom, Aston Villa host Spurs and West Ham face Cardiff.
The second round schedule was completed last night. Marouane Fellaini came on as substitute to snatch a 115th-minute winner as Everton edged Stevenage 2-1 after extra-time.
Cardiff saw off plucky Accrington 2-0 with goals from Nicky Maynard and Rudy Gestede. Aston Villa eased past League One Rotherham at Villa Park 3-0 with goals from Andreas Weimann, Christian Benteke and Fabian Delph.
Goals from Shola and Sammy Ameobi saw Newcastle win 2-0 at Morecambe while Watford beat Bournemouth 2-0.
Kenwyne Jones’s hat-trick saw Stoke past Walsall 3-1 while a 94th-minute goal from Jamaal Lascelles saw Nottingham Forest edge Millwall 2-1 after extra-time.
Capital One Cup third round draw: Manchester United v Liverpool. Sunderland v Peterborough. West Ham v Cardiff. Man City v Wigan. Burnley v Nottingham Forest. Newcastle v Leeds. Southampton v Bristol City. West Brom v Arsenal. Swindon v Chelsea. Tranmere v Stoke. Watford v Norwich. Aston Villa v Tottenham. Hull v Huddersfield. Leicester v Derby. Birmingham v Swansea. Fulham v Everton.
* Matches to be played September 24/25.