This cause has two chances: fat and slim. Savonarola started out as a holy and inspiring monk. He then made the mistake of getting involved in Florentine politics and eventually openly defying the Pope. “My Kingdom is not of this world” is usually a good guide for clerics to follow, absent extraordinary circumstances.

We are in Florence right now and went to the San Marco Museum on December 11, where we were told about this monk. Such a coincidence!
Believe it or not, the great Fr. Garrigou-Lagrange (r.i.p.) himself weighed in on the Cause for Savonarola, sometime back in the 1920’s (I think). This was at the preliminary stage, when certain Dominicans were trying to get him rehabilitated (since he had been condemned by a Canonical court at the time of his execution). They were, of course, successful.
I’m not sure what progress has been made with his cause since then. He was disdainful of the papal condemnation of his preaching, because it was widely believed at the time (and proven since?) that the reigning Pope, Alexander VI Borgia, had bribed the electors. Therefore, his election was null and void and without effect (in theory). Even Isabella and Ferdinand publicly rejoiced at news of the Pope’s death–the bells were rung throughout the Kingdoms!
Savonarola was of impeccable morals in his private and priestly life, by all accounts. His public (and private) enemies do him credit. He certainly excoriated some of the worst figures of Renaissance Italy. His crossing from private to public life is not without precedent: St. Bernard of Clairvaux, St. Norbert, and even St. Ambrose all defied papal and kingly bad behavior when warranted.
In other words, the jury is still out on his canonization, as far as I can tell.
Regardless of merits (and they are questionable), the current Vatican will not eagerly rehabilitate a man who railed against papal and curial corruption. Strikes too close to home.
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Roberto Ridolfi’s famous bio of Savonarola has an appendix tracing the history of S’s cause; it began shortly after his death, and has continued, on and off, since then. I can think of considerably worse people to canonize than Savonarola.