The Northern Irishman's side were drawn to play either Crusaders or the Norwegian outfit in the second qualifying round of the Europa League. Wright is gearing up for his first season as McDiarmid Park boss after replacing fellow Northern Irishman Steve Lomas as manager.
But the former Distellery chief claims old rival Stephen Baxter and his Belfast Reds face a tough job in their first-round tie. Wright said: "I was thinking this morning that it would be quite ironic if my first game in charge was against a Northern Irish side. It would be nice to go back if it was Crusaders. But we can't second guess things."
St Johnstone will travel to either Northern Ireland or Norway for the first leg on July 18 before hosting the return on July 25. Hibernian, meanwhile, have been drawn to take on either Drogheda from Ireland or Malmo of Sweden.
The Scottish pair will have to make their way through two further qualifying rounds to reach the group stage of the competition. The ties they have been handed for the second round look potentially very tricky, though, and the same can be said for Irish club Derry City, who face Turkey's Trabzonspor.
Crusaders-Rosenborg, Drogheda-Malmo and the rest of the first qualifying round clashes will take place with the first legs on July 4 and second legs on July 11. The draws for both stages were made earlier on Monday, and there were six other teams from Britain or Ireland involved.
In terms of Welsh sides, Airbus UK meet FK Ventspils of Latvia in round one, with the winners then playing Luxembourg's Jeunesse Esch or Finland's TPS Turku in round two.
Prestatyn face another Latvian outfit in SK Liepajas Metalurgs for the right to take on Croats HNK Rijeka, and Bala are up against Estonia's Levadia Tallinn and then, if they beat them, Pandurii Targu Jiu of Romania.
There are two more teams from Northern Ireland in action - Glentoran meet Icelanders KR Reykjavik, with Belgium's Standard Liege awaiting the victors, and Linfield have been paired with IF Fuglafjordur from the Faroe Islands, the winners then facing Xanthi of Greece in round two.
Meanwhile, Ireland's St Patrick's Athletic will go head to head with VMFD Zalgiris of Lithuania, with the winning side then meeting either FK Teteks (Macedonia) or FC Pyunik (Armenia).