The tie is the standout of the round and sends Roberto De Zerbi's side to Anfield weeks after the clubs' Premier League meeting. Spurs advanced with a 5-1 win over Charlton earlier in the evening.
Coventry City were paired with Aston Villa, while Newcastle, 3-2 winners over West Bromwich Albion, travel to Millwall. Holders Manchester City host Norwich City.
The nine Premier League clubs in European competition entered at this stage, with Manchester United facing Brighton, Premier League champions Arsenal heading to Ipswich Town, Bournemouth hosting Lincoln City, Sunderland meeting Hull City and Crystal Palace taking on Middlesbrough.
Everton, 4-0 winners at Preston on Wednesday, host Wolves. Bradford City, who knocked out Burnley on penalties, travel to Leyton Orient. Leeds United await the winners of Thursday's tie between Chelsea and Luton Town, and West Ham face either Fulham or AFC Wimbledon.
A pre-draw determined home and away status for the eight Champions League and Europa League clubs, who could not be drawn together, with six at home and two away.
The ties are scheduled for September.
EFL Cup third round draw:
Crystal Palace v Middlesbrough
Manchester United v Brighton
Manchester City v Norwich City
Sunderland v Hull City
Ipswich Town v Arsenal
Coventry City v Aston Villa
Bournemouth v Lincoln City
Liverpool v Tottenham
Chelsea or Luton v Leeds United
Millwall v Newcastle United
Fleetwood Town v Sheffield United
Everton v Wolves
Leyton Orient v Bradford City
Reading v Brentford
Peterborough United v Barnsley
West Ham United v Fulham or AFC Wimbledon