French midfielder Pogba was transferred for more than £89.3 million ($111 million, 105.2 million euros) in August 2016 from Italian club Juventus.
Confirmation of the investigation came after French media reports said FIFA had opened an inquiry.
It is not yet clear what aspect of the transfer FIFA is investigating.
Pogba, 24, 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.
He flourished 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.