Premier League leaders Chelsea will host Notts County or Peterborough, English champions Leicester City will visit fellow top-flight side Everton, while Liverpool welcome Newport County or Plymouth Argyle in ties to be played between 6-9 January.
Arsenal, who like Manchester United have won the famous old trophy a record 12 times, travel to Preston North End, while north London rivals and eight-times winners Tottenham Hotspur entertain Aston Villa, who won the FA Cup on seven occasions.
Seventh-tier Stourbridge United, the lowest ranked team left in the competition, face a rearranged second-round tie at home to Northampton Town on 13 December before they can contemplate a visit to league Two (fourth-tier) Wycombe Wanderers.
There are four all-Premier League ties, including Hull City at home to Swansea City and Burnley away to Sunderland.
Second-tier Reading’s boss Stam was a favourite during three years at United, where the Netherlands international was part of the famous 1998-99 treble-winning side under Alex Ferguson. He also won league titles either side of that historic season.
Stam’s ex-United team mate Andy Cole expects the Dutchman to get a good reception on his return to Old Trafford.
“I look forward to that,” he told the BBC. “He’s done very well at Reading. I’m really pleased for him.”