The conflicts in the Ukraine and Syria are likely to dominate the talks, organised on the sidelines of a visit to Milan 2015 expo's Russian pavilion.
Putin, a champion of conservative values who denounces gay marriage and derides the West's ways, has been cold-shouldered by the United States and much of Europe over Russia's role in the Ukraine crisis but seeks an ally in the Argentine pontiff.
It will be their second meeting. The first in 2013 was hailed a success by the Russian leader, who was chairing the G20 and was asked by Francis to find a diplomatic solution to the Ukraine situation without external military intervention.
"Putin wants to throw off his status as pariah. And he hopes that will work with the pope," said Russian historian and religious studies scholar Boris Falikov.
"But Putin's miscalculated," he added, surmising that the pope will say "Russia's policy in Ukraine is frowned upon by both the Vatican and him personally.