Russia has been confronted by corruption scandals and stadium delays in recent months.
"The head of state will meet the FIFA president in Moscow," read a brief statement from the Kremlin, with Infantino on his way to Kazan for the draw for next year's tournament.
On Wednesday, Infantino held the first of a series of regional meeting with federation chiefs outside Paris and underlined his desire to expand the World Cup finals beyond its current 32-team format.
"We see these World Cups as a chance, an opportunity to open parts of the world to an event," said Infantino, as Russia prepares to host the 2018 edition before Qatar takes centre stage in 2022.
Russia has been confronted by corruption scandals and stadium delays in recent months, but Putin guaranteed that everything will be ready on time for the 2018 showpiece.
The Confederations Cup runs from June 17-July 2 and will be played in four cities -- Moscow, Saint Petersburg, Kazan and Sochi.
The eight-team competition features all six continental champions including Cristiano Ronaldo's Portugal and Chile, as well as world champions Germany and hosts Russia.