The TV channel said Putin had cancelled at least two engagements - a meeting in the Kremlin on "civilian microelectronics" today, and a "Mentor" forum held on Wednesday.
This is the first meeting between Infantino and Putin since Vitaly Mutko decidedlast December to step down as head of World Cup Host Organizing Committee.
With four months to go before the football World Cup, both Russian Federation and FIFA want to avoid any surprises.
The talks were initially scheduled to take place at Putin's residence in the Black Searesort of Sochi.
Russian President Vladimir Putin on Monday met with Federation Internationale de Football Association chief Gianni Infantino in Moscow to discuss preparation works for the upcoming World Cup, the Kremlin said.
Russian news agencies say Infantino offered his condolences to Putin over the weekend's tragedy.More news: Trump asks Democrats to negotiate on infrastructure plan
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This is stated in the official press Secretary of the White house Sarah Sanders, released on Monday the results of the conversation.
Mr Putin will run as an independent and hopes to extend his rule to 2024, by which time he will have been president or prime minister for a quarter of a century.
A general view shows Volgograd Arena, the stadium under construction which will host matches of the 2018 FIFA World Cup, in the city of Volgograd, Russia February 2, 2018.
The country has been building and modernising facilities in preparation for the tournament, with a budget of about 11 billion dollars.
On a trip to Vietnam last week, Infantino said that "we'll experience the best World Cup ever this summer in Russian Federation".