As might be well-known to some, and perhaps especially to Catholics, the name of Saint Malachy, a former Archbishop of Armagh, is often associated with the Prophecy of the Popes. Much of the recent interest in this prophecy appears not to come from within Catholicism itself. Is there a general consensus from within Catholicism on this seemingly important issue?
There is no consensus, because there is hardly any discussion about this in official Catholic circles. For eg. a google search on the vatican website for "prophecy of the popes" (in quotes) or "prophecy of malachi" (in quotes) or "prophecy of saint malachi" (in quotes) yields no relevant results. On the other hand you will find huge discussion on things like the prophecies of Fatima, the revelation to Sr Faustina and so on.
It seems the official Catholic Church doesn't give so much weight to this prophecy. catholic.com, which is the largest Catholic apologetics site in the world says that "The consensus among modern scholars is that it is a 16th-century forgery created for partisan political reasons".
Public Revelation as the Church defines it, ended with the death of the last Apostle, St. John. All revelations since then are in the domain of Private Revelation. Thus the Prophecies of the Popes falls into this category. The question as to whether or not it is a forgery is not in this answer. Any vision or apparition must always be free of any errors of faith and morals. In order to safeguard the faithful, the Church has established some norms to be followed in the discernment as what constitutes a vision that may be believed.
As a general rule Rome rarely pronounces on a particular revelation and lets the local bishops pronounce their decisions. Since these prophecies were discovered at Rome and the Holy See has not pronounced a negative decision on this matter, it may be assumed that the faithful may believe in them or not.
Perhaps the popularity of other revelations such as Fatima (1917), Lourdes (1858), or to St. Faustina (1905-1938) gave rise to the Vatican to make a declaration that these particular private revelations are "worthy of belief".
Also, these prophecies touch the very nature of each Pontiff in a personal way. Each successive Pope has chosen not to speak out on this subject and has chosen to let the prophecies run their course! Thus, I conclude no official statement will ever be pronounced on this subject and one will always be free to believe them or not. Rome simply puts little stalk into them.