The Owls were held to a first round goalless draw by Plymouth Argyle on Sunday and have been confirmed to face a replay at Home Park on Tuesday 16.
Whoever wins out in that match-up will visit either Rochdale or Notts County in the second round before the Premier League big guns are thrown into the hat at the following stage.
A match against Rochdale would see Wednesday head to Spotland for the second time in as many season after their League Cup outing there last season. It would also see Darren Moore go up against a former Owls player in Robbie Stockdale, who spent time on loan at Hillsborough in 2000.
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Rochdale also have former Wednesday youngster Conor Grant among their ranks.
Wednesday’s last competitive match against Notts County – now in non-league under the tutelage of highly-rated young manager Ian Burchnall – came courtesy of a League Cup win in 2014.
“It will be a challenge,” Moore told reporters on Sunday after their long trip to Plymouth was confirmed.
“We will get back in tomorrow and our training programme will change because of the replay. You've got to look at the training and the travel. We will have to take that into consideration. We will have to look ahead at games and readjust for it.
“We are still in the FA Cup and we have got an opportunity to progress to the second round.”