A senior source in the prime minister's office told United Press International Sharon is "positively considering" the invitation.
Israel and Tunisia never had full diplomatic relations, and the little they did have petered out during the Palestinian uprising.
The invitation concerned a visit to attend the World Summit on the Information Society.
The Yediot Aharonot newspaper, which broke the story, said Israeli Foreign Minister Silvan Shalom has been holding secret contacts with his Tunisian counterpart, Abdelbaki Hermassi, in an attempt to establish diplomatic ties.
Shalom was born in Tunisia.