The Swans will face Scottish side Hibernian or Malmo of Sweden as they return to European competition after a 22-year absence thanks to last season's Capital One Cup success.
If Swansea are to enter an all-British tie, Hibs will need to overturn a 2-0 deficit when they host Malmo in the second leg of their second qualifying round clash next Thursday.
Swansea will stage the first leg of the tie at their Liberty Stadium home on August 1, before making the trip to Scotland or Sweden the following week.
The Welsh club will also need to get through a play-off round if they are to make the group stage of the tournament.
While Hibs and Malmo, who were European Cup runners-up to Nottingham Forest in 1979, will provide potentially tricky opposition, Laudrup is delighted his side have avoided any long-haul journeys.
"I'm pleased with the draw," the Dane told www.swanseacity.net. "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.''
Malmo would appear to be Swansea's likely opponents, but Laudrup is not ruling out a Hibs comeback.
"Malmo is a huge club in Sweden with a proven record and proud history,'' he said. "But I'm sure Hibernian will be in there fighting until the end.''