The Owls have been placed in Group H of the Northern section of the draw alongside fellow League One side Burton Albion and ambitious League Two outfit Bradford City.
Both sides are managed by legendary Premier League forwards. Burton finished 16th in the third tier under former Leeds United and Chelsea man Jimmy Floyd Hasselbaink, while Manchester United icon Mark Hughes took the reins at Bradford in February.
Groups have been designed to cut down on travel time and offer the best possible recovery time for players.
On Thursday the groups will be made whole with the addition of one of the under-21 sides from Everton, Leeds United, Leicester City, Liverpool, Manchester City, Manchester United, Newcastle United or Wolverhampton Wanderers making up each group.
Fixture dates and venues will be confirmed soon afterwards, with each club set to play each other once.
The much-maligned competition offers clubs the opportunity to earn a place at a Wembley final, as the Owls’ near-neighbours Rotherham United did last season when they won out against fourth tier Sutton United.
Wednesday’s Papa Johns run ended in the second round last season when after a breezy time in the group stage they suffered a shock 3-0 defeat to Hartlepool United.
Thursday will be a busy day for the fixture compilers. Alongside the confirmation of Wednesday’s fourth Papa Johns opponent, the League One fixture schedule will be confirmed as well as the draw for the League Cup.