Citing people familiar with the matter, Bloomberg reported on Friday that EU officials informed member states' ambassadors on Wednesday that diplomats had started work on potential measures against Ben-Gvir, despite continuing divisions among the bloc's member countries.
The report said discussions remain at an early stage and are taking place behind closed doors. A spokesperson for the European Commission did not immediately respond to Bloomberg's request for comment.
Israel attacked the Gaza-bound Global Sumud humanitarian flotilla in international waters in mid-May. Live broadcasts from the flotilla showed Israeli naval forces intercepting the vessels.
A video later circulated by Israeli authorities showing Ben-Gvir walking among detained activists who were kneeling in tightly packed formations while zip-tied, drawing widespread global criticism.
Ben-Gvir appeared in the footage waving an Israeli flag and taunting detainees. All activists were later released following international backlash.