Meanwhile Sunderland travel to Arsenal.
Middlesbrough are at home to Burnley, and Hartlepool (if they beat Salford in a replay) will play Derby County.
Part-timers Whitehawk have been handed a possible trip to Everton in the draw for the third round of the FA Cup.
The sixth-tier side, who are on their best run in the competition in their history, will make the trip to Goodison Park if they get through their second-round replay against Sky Bet League Two Dagenham & Redbridge at home.
The third-round draw, made on Monday night in Cardiff, also sees Jurgen Klopp's first FA Cup tie as Liverpool boss take him to League Two Exeter.
Whitehawk were one of four non-league teams to feature in the draw.
The lowest-ranked among them, Salford City, will host Championship high-fliers Derby if the seventh-tier outfit get past Hartlepool in their second-round replay.
Eastleigh, the only one of the quartet to have made it through outright, were handed a home tie against Championship basement boys Bolton, while the draw also pitted the winner of Grimsby's second-round clash against Shrewsbury - being played on Monday night - against Cardiff away.
As well as the Arsenal-Sunderland game, there are four other all-Premier League ties, with the pick seeing surprise leaders Leicester travelling to fifth-placed Tottenham.
The others are Norwich v Manchester City, Southampton v Crystal Palace and Watford v Newcastle.
Manchester United host League One Sheffield United and Chelsea will play the winner of Leyton Orient v Scunthorpe at Stamford Bridge.
Other notable fixtures include rock-bottom Premier League side Aston Villa's trip to Wycombe, who reached the 2001 semi-final, and Leeds' clash with Rotherham at Elland Road, where respective managers Steve Evans and Neil Redfearn will both be facing their old clubs.
That game is one of six all-Championship matches in the draw.
Whitehawk manager Steve King had admitted before the draw that he was hoping to be given the chance to take on Liverpool.
And afterwards, regarding the prospect of facing Everton instead, King told the BBC: "I wanted the Reds but I got the Blues. But we ain't got the blues."
He added: "It's a tough game to get through against Dagenham & Redbridge first because both teams will want to play that massive tie.
"It's 50-50, the best on the day goes through."
The ties will be played between January 8 and 11.
Watford v Newcastle
West Brom v Bristol City
West Ham v Wolves
Salford or Hartlepool v Derby
Exeter v Liverpool
Tottenham v Leicester
Colchester v Charlton
Peterborough v Preston
Northampton v MK Dons
Arsenal v Sunderland
Newport v Blackburn
Ipswich v Portsmouth
Birmingham v Bournemouth
Wycombe v Aston Villa
Sheffield Wednesday v Fulham
Oxford v Swansea
Brentford v Chesterfield or Walsall
Bury v Bradford
Manchester United v Sheffield United
Everton v Dagenham or Whitehawk
Southampton v Crystal Palace
Eastleigh v Bolton
Nottingham Forest v QPR
Carlisle v Yeovil
Chelsea v Leyton Orient or Scunthorpe
Doncaster v Stoke
Leeds v Rotherham
Cardiff v Grimsby or Shrewsbury
Huddersfield v Reading
Middlesbrough v Burnley
Norwich v Manchester City
Hull v Brighton