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.
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.
Draw in full:
