Lawyer Hacı Ali Özhan says he has written to Portuguese leaders seeking permission for Mehmet Ali Ağca to travel there for the May 13 event.
Ağca was released from prison in January after completing a sentence for the 1979 killing of a journalist.
Ağca shot John Paul on May 13, 1981, in St. Peter's Square in Vatican City, during a period in which he had escaped from prison.
Three shepherd children claimed in 1917 to have seen the Virgin Mary in Fatima and that she made predictions.
Church officials said in 2000 that she foretold the assassination attempt.