The sources identified the two journalists as Sefian Shawarbi and Nazir al-Qatari.
The pair was kidnapped in Libya last September while working for a television channel.
Tunisian authorities have yet to comment on claims that the two had been executed.
Online activists have shared photos showing the two journalists being led by an unidentified gunman.
"Footage showing the rule of God being applied to media people who work for a TV channel hostile to Islam and which spreads corruption," reads a caption below the photo.
Libya has remained in a state of lawlessness since the 2011 ouster and death of strongman Muammar Gaddafi.