Depends on what the Pope himself wants, I imagine. Not every head of state or head of government wants to hold foreign citizenship.
Two examples from Canada: former Governor General Michaëlle Jean, who represented the Canadian monarch in Canada for day-to-day head of state duties, renounced her French citizenship when before becoming Governor General; and current Canadian Prime Minister Mark Carney renounced his British and Irish citizenships before becoming Prime Minister. Neither renunciation was required according to law or constitutional convention, but they both wanted to remove any question as to their allegiance.
Two examples from Canada: former Governor General Michaëlle Jean, who represented the Canadian monarch in Canada for day-to-day head of state duties, renounced her French citizenship when before becoming Governor General; and current Canadian Prime Minister Mark Carney renounced his British and Irish citizenships before becoming Prime Minister. Neither renunciation was required according to law or constitutional convention, but they both wanted to remove any question as to their allegiance.