League Two Newport County or Plymouth Argyle will travel to Anfield to face Premier League Liverpool in the FA Cup third round.
West Ham will host Manchester City in the pick of the all-Premier League ties, with Everton set to welcome Leicester City.
Holders Manchester United will welcome Reading, managed by former United defender Jaap Stam.
National League Sutton United will face neighbours AFC Wimbledon.
The 32 third-round ties will be played across the weekend of 6-9 January 2017.
Newport are a fan-owned club and chairman Gavin Foxall said of the prospect of a tie at Anfield: “It would absolutely be a massive financial boost for us.
“Certainly for a club like ours it would secure the future for a season or two at least.
“A game at Anfield against Liverpool would rank right up there in the club’s history.”
There are four all-Premier League ties, including Hull City against Swansea City while Burnley travel to Sunderland.
Former Manchester United striker Andy Cole expects Dutchman Stam to get a good reception on his return to Old Trafford.
“I look forward to that,” he said. “He’s done very well at Reading. I’m really pleased for him.”
The lowest ranked club left in the competition, Stourbridge United, face a potential trip to League Two Wycombe Wanderers, should the seventh-tier Northern Premier League Premier Division club beat Northampton Town in a rearranged fixture.
Of the other non-league sides through to the third round, Barrow will visit Rochdale while either Halifax or Eastleigh go to Brentford.
“I think the chairman will be really happy, because at least we’re at home,” said Barrow manager Paul Cox.
FA Cup third-round draw:
Ipswich Town v Lincoln
Barrow v Rochdale
Manchester United v Reading
Hull v Swansea
Sunderland v Burnley
QPR v Blackburn
Millwall v Bournemouth
West Ham v Manchester City
Brighton v MK Dons/Charlton
Blackpool v Barnsley
Wigan v Nottm Forest
Birmingham v Newcastle
Chelsea v Peterborough/Notts County
Middlesbrough v Sheff Weds
West Brom v Derby County
Everton v Leicester
Liverpool v Newport/Plymouth
Wycombe v Northampton/Stourbridge
Watford v Burton Albion
Preston v Arsenal
Cardiff v Fulham
Stoke v Wolves
Cambridge Utd v Leeds
Bristol City v Shrewsbury/Fleetwood
Huddersfield v Port Vale
Tottenham v Aston Villa
Brentford v Halifax/Eastleigh
Bolton v Crystal Palace
Norwich v Southampton
Sutton Utd v AFC Wimbledon
Accrington v Luton
Rotherham v Oxford/Macclesfield