Today, Neil Druckmann, Creative Director at Naughty Dog, confirmed in a tweet that The Last of Us Remastered will be pushed to 60 frames per second. He also mentioned that the port is being developed internally by Sony's first party studio.

For those asking, @Naughty_Dog is developing The Last of Us Remastered and we're targeting 60fps. More info to come. #PS4

Expected release for the remastered version will be sometime this summer.