In a statement, the Bulldogs said: "The club has today been made aware of alleged images surfacing on social media of a current player taken several years ago.
"The club has informed the NRL Integrity Unit of the matter. The club is not in a position to comment further at this time."
An NRL spokesman told the Daily Mail Australia it is aware of the video and will be investigating.
Napa won the premiership with the Roosters last year but made the move to the Bulldogs for the 2019 season.
He joined the club on a three-year deal, replacing former Bulldogs prop David Klemmer, who has moved to Newcastle.
Napa debuted for the Roosters in 2013 and before heading to Belmore, had spent his entire NRL career at the Bondi club.
He played 122 matches for the Tri-Colours, during which time he made a name for himself as one of the biggest hitting forwards in the competition.
He's played five Origins for the Maroons.
The NRL integrity unit was also involved in South Sydney star Sam Burgess' lewd photo scandal last year.
This was after a complaint was made by a woman alleging Rabbitohs players exposed themselves to her on Facebook following the Rabbitohs' victory over the Warriors at Mt Smart Stadium in May.