Do Italian consumers value health claims on extra-virgin olive oil?

•Respondents valuing the organic clue are also interested in EVOO with health claims.•Consumers with a higher general interest in health value health claims on EVOO.•EVOO with health claims is of interest to those willing to use food as medicine.•Exposure to diseases led to a consumer appreciation of health claims on EVOO.•The market of EVOO with health claims is a potential niche market.