Let's be cautious here but a cached version of a Rockstar FAQ for the next-gen version of GTA 5 supposedly mentions a first person view for the game, both on foot and in cars.
The cache is gone now which in itself is curious as the 404 page currently displayed usually requires the site's owner to remove it. Several news outlets are reporting seeing it however. As well as "across-the-board graphical and technical improvements" it also mentions, "A brand new first person mode for vehicles that shows the interior of the vehicle, including working speedometers, tachometers, dash lights, and more", and, "A brand new first person mode while on foot".
It's a rumour but an interesting one. The post was dated for September 12th when a slightly different next-gen FAQ went live, which suggests even if the information was true, it's out of date and could reference a feature that's been cut.
We've already seen what a first person GTA 5 would look like via modders:
GTA 5 is out on PS4 and Xbox One on November 18 and later on PC, in January 2015.