Jamie Raskin, the highest-ranking Democrat in the House Judiciary Committee, has written to Infantino, requesting information and communications by August 9 on the relationship with Trump and his administration, and on ticketing at the recent World Cup.
Raskin also asked Infantino to make himself available for questioning by the judiciary committee when he is in the US.
The Democrats said "the investigation examines a sustained campaign by FIFA to secure special favours from President Trump ... all while gouging American consumers for exorbitant prices during the World Cup", which the US co-hosted with Mexico and Canada.
According to New York Times sources, the probe could become a formal investigation if the Democrats reach a majority in the November elections, and Raskin could potentially become judiciary committee chairman.
In his letter, Raskin cited a "hilariously fake" FIFA Peace Prize which Trump received from Infantino at the World Cup draw in December.
He criticised FIFA for leasing an office space in New York's Trump Tower which would only be used for the duration of the World Cup and had a market value of $600,000 a year.
"These actions appear designed to induce President Trump and his administration to make decisions in FIFA's favour," Raskin said.
Raskin added: "The most recent quid pro quo that FIFA and President Trump orchestrated is not a victimless crime. It hurts Americans.
"FIFA has taken its newfound favoured status in the Trump Administration as a sign that it may rip off its consumers, most notably, by employing illegal price gouging and fraudulent sales tactics for the World Cup."
Dynamic pricing was introduced for the first time at a World Cup, with cost set by demand. Apart from inflated prices, FIFA is accused of placing ticket holders in other sections of a stadium than those for which they had bought tickets.
Ticketing practices are under investigation by the attorney general in New York and New Jersey.
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