Russia is bidding against England, the United States, and combined bids by Spain and Portugal and by Belgium and the Netherlands for the 2018 tournament.
Those same bidders, as well as Qatar, Australia, Japan and South Korea, are also up for 2022.
"If we get the honour (of staging the 2018 finals) we can offer additional government guarantees regarding visa-free entry for participants and guests," Putin told visiting officials from FIFA, football's world governing body.
The FIFA inspection team is visiting four Russian cities - Moscow, St Petersburg, Sochi and Kazan - this week.
The Russian government waived entry visa requirements for fans with valid tickets for the 2008 Champions League final between English clubs Manchester United and Chelsea in Moscow.
In April, Putin signed Russia's World Cup guarantees for a wide range of issues including security, tax and customs breaks.
On Tuesday, he assured FIFA officials that Russia would have all the relevant World Cup infrastructure ready in time for the 2018 tournament.
"We will have everything ready on time, using both state and private capital. We would stage (the tournament) at the highest possible level, I have no doubt about it," he said.
FIFA will announce the 2018 and 2022 hosts in December.
