The Frenchman moved to the club last summer for £89m to become the most expensive player in the history of the sport.
Fifa have asked United for "clarification on the deal", the AFP news agency says, though it remains unclear what details are under scrutiny.
This follows reports that the midfielder's agent, Mino Raiola, is set to make £41m from the transfer. Leaks suggest that Raiola acted on behalf of Manchester United, Juventus and Pogba, contravening Fifa's rules governing transfers, according to French outlet Mediapart.
In a recently published book, ‘Football Leaks: the Dirty Business of Football’, Raiola's extraordinary earning power is laid bare.
According to the book, based on the research of Der Spiegel journalists Rafael Buschmann and Michael Wulzinger, the so-called 'super-agent' was handed a £23m cut of the initial transfer fee and will receive five instalments totalling £16.39m over the course of Pogba's five-year contract.
The 24-year-old started his career with the English club but made just three appearances in the Premier League before heading to Italy, after an apparent falling out with then manager Alex Ferguson.
The Frenchman went on to flourish in Serie A, winning four league titles with Juventus between 2012 and 2016.
Pogba also appeared in the 2015 Champions League final, which Juventus lost 3-1 to Barcelona.
At the same time, the powerful midfielder made himself a mainstay of the French national team.
He made his debut in March 2013, just a week after his 20th birthday, in a World Cup qualifier against Georgia.
He also featured as part of the 2014 French World Cup squad and was named the tournament's best young player.
Pogba's performances at the 2016 European Championship helped attract the attention of his former club Manchester United, under new manager Jose Mourinho.
After a protracted transfer saga, lasting several weeks, Pogba eventually signed for United last August and has so far appeared in almost 50 league and cup games this season.
Additional reporting by AFP.
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