The inquiry is trying to establish if there was an undue influence on the decision to block Qatar Airways’ bid for more flights into the country.
2GB’s Ben Fordham exclusively revealed the photo of Joyce, who is sitting on a park bench with his pet dog while using his phone.
It’s not known what park he was sitting at.
Joyce landed at Sydney Airport in February after having spent five months with family in his native Dublin.
Vanessa Hudson became Qantas’ new CEO in November last year, taking over from Joyce.
Hudson is the 13th CEO in the airline’s 103 year history and the first woman.