Suarez could return at Man United in League Cup
The Uruguayan has missed the start of the Premier League season as he serves the remainder of a 10-match ban for biting Chelsea's Branislav Ivanovic during a 2-2 draw at Anfield in April.
Suarez has constantly been linked with a move away from Anfield during the transfer window, with fellow Premier League side Arsenal having two bids rejected.
But Liverpool rejected those overtures, and his punishment expires before the encounter with fierce rivals United at Old Trafford, and Brendan Rodgers may be tempted employ the 26-year-old.
Elsewhere, Newcastle United were handed a difficult tie as they will welcome Leeds United to St James' Park.
Alan Pardew's side left it late to overcome League Two side Morecambe 2-0 in round two, while Leeds ensured their progress with a 3-1 victory away to Doncaster Rovers.
Aston Villa were rewarded for their 3-0 victory over Rotherham United with a home fixture against Andre Villas-Boas' Tottenham, while West Ham will meet Cardiff City at Upton Park in a repeat of their opening game of the Premier League season.
League One outfit Bristol City beat Crystal Palace 2-1 in round two, and they once again face Premier League opposition when they travel to St Mary's Stadium to take on Southampton.
Other highlights include an all top-flight encounter between Fulham and Everton, while Midlands rivals Leicester City and Derby County will face off at the King Power Stadium.
Draw in full:
Manchester United v Liverpool
Sunderland v Peterborough United
West Ham v Cardiff City
Manchester City v Wigan Athletic
Burnley v Nottingham Forest
Newcastle United v Leeds United
Southampton v Bristol City
West Brom v Arsenal
Swindon Town v Chelsea
Tranmere Rovers v Stoke City
Watford v Norwich City
Aston Villa v Tottenham
Hull City v Huddersfield Town
Leicester City v Derby County
Birmingham City v Swansea City
Fulham v Everton