The footage from Putin's reception office was released by football's world governing body in a tweet featuring legends of the beautiful game juggling the ball and doing tricks.
The clip ended with Putin heading one back to Infantino after a heavily edited kickabout set to Rimsky-Korsakov's Flight of the Bumblebee.
"Some people just can't wait for the greatest show on earth," FIFA said in the tweet.
Others playing around with the official Telstar 18 World Cup ball included ex-England midfielder Wayne Rooney and Argentina's Diego Maradona.
Brazil's Ronaldo juggled by the beach while Sweden's Thomas Brolin had his fun in the snow.
Putin is an all round sports fan who is hoping to use the June 14-July 15 competition to showcase Russia and boost its image at a time of frayed relations with the West.
The games will be played in 11 spruced up host cities stretching from Russia's western exclave of Kaliningrad near Poland to Yekaterinburg in the Urals.
"It is important to show Russia the way it really is: open, hospitable and modern," Sports Minister Pavel Kolobkov said.
- 'Open heart' -
Russia's preparations for the most watched event in sports are going largely according to schedule but still being clouded by scandal and global disputes.
Fan violence that made Russians infamous at the Euro 2016 in France returned last month during a Europa League match in Spain between Spartak Moscow and Athletic Bilbao.
Organisers hope the February 22 insident in which a handful of Russians were arrested and a policeman died of a heart attack does not frighten away foreign fans.
Tensions with the West have been compounded by the ignomy of Russians being forced to perform under a neutral Olympic flag at the Winter Games in Pyeongchang over doping allegations.
The scandal forced former sports minister Vitaly Mutko to quit his post as chief World Cup organiser to focus on his appeal against a lifetime Olympic ban.
Mutko on Tuesday lost his remaining World Cup position as government representative to the organising committee.
"There was no and will be no state (doping) programme," Mutko insisted on Tuesday.
National team coach Stanislav Cherchesov said he hoped the World Cup would help foreign visitor ignore all the controversies and discover the real Russia.
"The most important thing is to come to Russia with an open heart and to try to understand our country and the places you are visiting," Cherchesov said in an interview released by FIFA.
"As we say in Russia, better to see something once than to hear about it a hundred times."
The tournament kicks of when Russia hosts Saudi Arabia in Moscow's renovated Luzhniki Stadium on June 14.
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