According to Swedish daily newspaper Dagens Nyheter, the Ethiopian government's pardon committee ordered a report into Johan Persson and Martin Schibbye's behaviour in the Kality prison.
"If it is correct that a formal request has been placed, that is very good news. It is one of the many steps that must be taken before a pardon can be carried out," the Norwegian professor and expert on Ethiopia Kjetil Tronvoll told TT.
Persson and Schibbye were arrested shortly after entering the conflict-ridden Ogaden province in July 2011. They were sentenced to 11 years' imprisonment in December and chose not to appeal the verdict.
Kjell, Persson's father, was in Addis Abeba on Tuesday to meet his son but had yet to hear the news.
"I do not want to comment until I know what this is about," he said.