The 44-year-old has previously expressed his admiration of notorious dictator Mussolini and labelled himself a fascist, though refuted claims his views are racist.
Labour MP David Miliband resigned from the Sunderland board because of the Italian’s “past political statements”, but while the club issued a strongly-worded statement in defence of their new manager, Di Canio himself has been reluctant to clarify his beliefs.
A Kick It Out statement read: “Football clubs have a responsibility to ensure that their employees demonstrate a commitment to anti-discrimination and equality of opportunity.
“It may be in the interest of both the club and Mr Di Canio to acknowledge a full and frank commitment to these policies.
“When fascism is referenced within the context of English football, there is a wider concern.”