"You did get an invitation to the ceremony. We hope that you will be able to attend," First Deputy Prime Minister Igor Shuvalov, speaking at a meeting of top government officials, was quoted as telling Putin by local media.
The Russian delegation will go to FIFA's Zurich headquarters in December when football's world governing body will choose the hosts for both events.
In July 2007, Putin, then Russia's President, played a key role in the International Olympic Committee's (IOC) decision to award the 2014 Winter Games to the Black Sea resort of Sochi.
"All of us still remember the work you did during our bid presentation to host the 2014 Olympics in Sochi," Shuvalov said.
Putin, speaking at Wednesday's meeting, urged the ministers to speed up work on the World Cup project which was unveiled in October last year.
"You had better start now, don't wait until the (necessary) paperwork arrives," Putin told Shuvalov.
Shuvalov said Russia's detailed bid book would be sent to FIFA on May 14.
Russia is bidding against Australia, England, Japan, United States, Belgium/Netherlands and Spain/Portugal for the rights to host the 2018 or 2022 finals.
Indonesia, Qatar and South Korea are bidding for the finals in 2022 only.
