Putin has previously met the pope's predecessor Benedict XVI as well as late pope John Paul II and there are hopes for what would be an historic meeting between a pope and a Russian patriarch.
Putin's predecessor Dmitry Medvedev, who is now the prime minister, met with Benedict XVI in 2011.
During another visit by Medvedev in 2009, the two states re-established full diplomatic ties which had been severed during Soviet times.
The Russian Orthodox Church has frequently used the Catholic Church of proselytising in Russia.
Pope Francis wrote to Putin in September as head of the G20 group of global powers to ask him to press for a political solution to the conflict in Syria without outside intervention.