Suarez, serving a 10-game suspension for biting Chelsea's Branislav Ivanovic last season, will be eligible for the match at Old Trafford scheduled for September 24 or 25.
The Uruguay striker is an unpopular figure at United after he was banned for eight games for racially abusing the club's defender Patrice Evra in 2011 and he inflamed the situation by refusing to shake the Frenchman's hand after making his return.
The third round also features a repeat of last season's FA Cup final as Manchester City take on Wigan Athletic, who were relegated from the Premier League after upsetting City to win at Wembley in May.
There are four other all-Premier League clashes as Fulham play Everton, Aston Villa host Tottenham Hotspur, West Ham United take on Cardiff City and West Bromwich Albion play Arsenal.
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 City visit second-tier Birmingham City.
Premier League Southampton host third-tier Bristol City, Leeds, winners in 1968, visit Newcastle United and Norwich City play Watford.
Leicester face local rivals Derby, Premier League Hull City host Huddersfield and four-times winners Nottingham Forest will face Burnley.
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 week commencing September 23rd.