Probably in two weeks or less.

In the last 200 years, the Catholic Church has diplomatically freed itself from all formal imperial influence in papal elections and dramatically sped up the process of holding a conclave. It usually takes ten to 15 days to gather the cardinals into conclave after the death of the pope, and they usually finish deliberating in just a few days. The last long conclave was in 1830–31 and lasted 51 days. Partly because of the organization of the supposed “St. Gallen Group,” the conclave to elect Francis was barely 28 hours old when it finished.