It's looking like the original Max Payne will be getting the PS2 Classic treatment on PS4, according to an ESRB listing.
While not officially announced, this seems very likely as Sony just released eight PS2 games on its latest console, including Rogue Galaxy, Mark of Kri, Dark Cloud, and some Grand Theft Auto games.
Furthermore, these titles were leaked for PS4 ports via the PEGI ratings board, so it wouldn't be surprising if history were repeating itself here.
The original Max Payne was released in 2001. The FPS cop drama spawned two sequels, 2003's Max Payne 2: The Fall of Max Payne, and Rockstar's 2012 follow-up Max Payne 3.