Liverpool could face either Leicester City or Arsenal in the fourth round of the Carabao Cup after the draw was held following the completion of round two on Thursday.
Leicester facing Arsenal is the only all-Premier League clash in the yet-to-be-played third round, with the winner of that match in line to face Liverpool should they beat Lincoln City in their third-round tie.
More round three matches featuring Premier League heavyweights include Manchester United-Luton Town, Chelsea-Barnsley, Tottenham-Leyton Orient and Manchester City-Bournemouth.
Not all Premier League sides have made it through to round three, however, as Wolves were eliminated after a 1-0 home loss to second-tier club Stoke on Thursday.
Burnley advanced to the third round after beating fellow Premier League side Sheffield United 5-4 in a penalty shootout following a 1-1 draw.
Lincoln or Liverpool v Leicester or Arsenal
Millwall or Burnley v Manchester City or Bournemouth
West Brom or Brentford v Fulham or Sheffield Wednesday
Fleetwood or Everton v West Ham or Hull
Bristol City or Aston Villa v Stoke or Gillingham
Leyton Orient or Tottenham v Chelsea or Barnsley
Newport or Watford v Morecambe or Newcastle
Preston or Brighton v Luton or Manchester United
The third round starts next week, with select matches available in the U.S. on ESPN+.