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"It can be believed probably and piously that the supreme Pontiff is not only not able to err as Pontiff but that even as a particular person he is not able to be heretical, by pertinaciously believing something contrary to the faith." (St. Robert Bellarmine, De Romano Pontifice, book 4, cap. vi)

This is my opinion, but it is not a matter of faith. Of course, Bellarmine's counsel about the theoretical possibility of a manifestly heretical Pontiff ought to be held together with his comments elsewhere:

Moreover, even though somewhere, by God's permission, a credulous people should be easily seduced by their pastor, no Catholic would dare say that therefore the people should be discouraged from obeying their prelates, or should themselves become judges of their pastors, and decide on the doctrine that is being preached to them. We know from present experience among the Lutherans that the danger of heresy is far greater by making this kind of concession to human liberty, than it will ever be from the simple obedience of the people. ("Tractatus de obedientia," in Auctarium Bellarminianum, ed. Le Bachelet (Paris, 1913), p. 385)