The 26-year-old's future has been the subject of speculation this summer after he began agitating for a move away from Anfield.
Should Suarez stay, his first match back after biting Chelsea defender Branislav Ivanovic last season will be at Old Trafford against United.
The clash is the pick of a third round to be played on September 24 or 25, when there will be a repeat of this year's FA Cup final.
Wigan shocked Manchester City to triumph in May and will travel to the Etihad Stadium hoping to cause another surprise in this year's Capital One Cup.
Jose Mourinho's first taste of the competition he twice won in his previous spell as Chelsea boss will be at Sky Bet League 1 outfit Swindon.
Holders Swansea start their defence at Birmingham, while there are a number of all Premier League ties. Arsenal are at West Brom, Aston Villa host Tottenham, West Ham face Cardiff and Fulham take on Everton.
Newcastle's reward for sneaking past Morecambe is a home clash with Leeds, while Sunderland take on Peterborough and Southampton welcome Bristol City.
Elsewhere, Tranmere travel to Stoke, Watford host Norwich, Hull welcome Huddersfield to the KC Stadium, Leicester take on neighbours Derby and Burnley host Nottingham Forest.
Draw in full:
Manchester United v Liverpool
Sunderland v Peterborough
West Ham v Cardiff
Manchester 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
Ties to be played the week commencing September 23.