The Capital One Cup holders will face either Scottish side Hibernian or Malmo of Sweden as they embark on their first European campaign in 22 years.
The more likely opponents are the Swedish side, who hold a 2-0 first-leg lead over Hibs in their second qualifying round tie, with the second leg next Thursday.
"I'm pleased with the draw," the Dane told the Swans' official website. "It was important for me that we avoided a long trip and the prospect of difficult weather conditions. Sweden or Scotland is perfect for us geographically.
"We also know the playing styles of both teams, so that is also a positive for us, although I would have preferred to be away in the first leg rather than home. But you can't have everything."
Swansea will stage the first leg of the tie at the Liberty Stadium on 1 August, before making the trip to Scotland or Sweden the following week.