There is no official Vatican online reference to this alleged miracle, so I did some basic research.
The first thing I noticed is that the details of the 1996 miracle vary according to the source of the story, with at least three variants as to where the host was found. This is typical of urban myths, but by itself that is not enough to disprove the story. The Australian Catholic Weekly, which is not an 'official' source, was asked whether Pope Francis had approved the miracle, and printed an article that says that Francis had investigated the claim before becoming pope. Whether or not Auxiliary Bishop Jorge Bergoglio (now Pope Francis) was impressed with what he was told, it appears that the pope is not moving to have this recognised as a miracle.
This article from Gospa Missions says, "Although this miracle awaits further confirmation in the Church ..." indicating that the Catholic Church has not (yet) accepted the purported miracle.
One source says that Professor John Walker, of Sydney University, had confirmed that the material given to him was human flesh. Sydney University publishes a list of academic staff and, although it reports no Professor John Walker, it appears that a Dr. John Walker had been on the University faculty until 1987, nine years before the supposed miracle, but he worked in medical parasitology. The late Professor
Frederick Zugibe is also credited with having tested the specimen and verified that it came from a living heart. This important investigation is not found in any of the biographies that I have found on Zugibe.
A post on the Catholic Answers forum claims the purported miracle to be a fraud, because the Higher Council of the World Health Organization, which supposedly confirmed the findings of Dr. Edoardo Linoli, does not exist.
One could ask why God would perform this obscure miracle in just this way, and the most plausible reason would be either to bring people back to the faith, or to assist the finances of a struggling church in Argentina.