The Potters received a bye during the first round, due to their Premier League status, and were seeded for the second round.
With two games to be shown live on Sky TV, the games date could be determined due to this if picked.
Thirteen Premier League teams enter the competition at this stage, along with Championship sides Newcastle and Middlesbrough who also received byes. The other seven Premier League teams enter in round three, when there are no seedings, and have the extra bye due to their participation in either the Champions League or Europa League.