The Owls or the Swans, who drew 0-0 at Hillsborough in their fifth round tie on Saturday afternoon have been paired at home to either Spurs or Rochdale who play at Spotland on Sunday (4pm).
Wednesday will travel to the Liberty Stadium to take on Carlos Carvalhal's side in their replay a week on Tuesday.
Elsewhere in the draw, Manchester United are at home to Brighton, Leicester City who beat Sheffield Uniuted on Friday night have been rewarded with a home tie against Chelsea.
Wigan or Manchester City will be at home to Southampton.
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Sheffield Wednesday or Swansea v Rochdale or Tottenham
Manchester United v Brighton
Leicester v Chelsea
Wigan or Manchester City v Southampton
Ties to be played over the weekend of March 16-19.