Both clubs are currently bidding for promotion from the third tier of English football, although Bolton have already beaten the Blades once this term, running out 1-0 winners on the opening day of the season.
Charlton Athletic will host MK Dons in another all-League One encounter, while ninth-tier side Westfields - the lowest-ranked club still in the competition - will host either Bury or AFC Wimbledon if they are able to get past Curzon Ashton in a first-round replay.
Newport County will face League Two rivals Plymouth Argyle if they are able to beat Alfreton Town in a replay, while Luton Town and Yeovil Town will meet in another all-League Two clash if the latter overcome Solihull Moors.
Victory in the second round would see clubs drawn alongside Championship and Premier League teams, who enter the competition at the next stage.
The matches in the second round will be played between December 2 and December 5.
FA Cup second round draw:
Westfields or Curzon Ashton vs. Bury or AFC Wimbledon
Chesterfield vs. Wycombe
Millwall vs. Braintree Town
Macclesfield vs. Oxford United
Bolton vs. Sheffield United
Blackpool vs. Gillingham or Brackley Town
Whitehawk or Stourbridge vs. Northampton
Boreham Wood or Notts County vs. Peterborough
Cambridge United or Dover vs. Coventry or Morecambe
Port Vale vs. Hartlepool
Bristol Rovers or Crawley vs. Barrow or Taunton
Woking vs. Accrington Stanley
Lincoln City vs. Oldham
Luton vs. Yeovil or Solihull Moors
Sutton United vs. Cheltenham or Crewe
Eastleigh or Swindon vs. Halifax or Dagenham and Redbridge
Shrewsbury vs. Southport or Fleetwood
Charlton vs. MK Dons
Plymouth vs. Newport or Alfreton
Carlisle vs. Maidstone United or Rochdale