Reports suggest that the Black Cats are showing considerable interest in the Saint-Etienne centre-back, who is the older brother of Manchester United's work record signing Paul Pogba.
Moyes has been after a new central defender after it became apparent that Everton were keen on Lamine Kone and it appears as though Pogba, 26, is now on his wish-list.
The Guinea international, who has been with Saint-Etienne since 2012, would reportedly cost Sunderland around £6.5million.
It is understood that Black Cats winger Adnan Januzaj, who is on loan from United, may have a role to play in luring Pogba to the Stadium of Light as he has a close relationship with the defender's more famed brother.
Hull City are also believed to be showing interest in Pogba.