Official sources.

While we now know that the official stance is a big "no" on story DLC (see above), things looked a little bit different in the past.

The reason why the community was so hyped up about some story DLC is because at one point Rockstar Games announced it.

Considering the massive success of GTA 5, it wasn't even surprising. Though certain events at the end of the story meant that Rockstar would need to set the DLC during the course of the existing story, or canonize one of the three possible endings, it seemed like a logical evolution for the game.

As for the exact content of the scrapped DLC, we can't say for sure.

The source code of certain GTA Online DLCs contain a lot of leftovers that make it seem like they were originally planned for single player DLC, most notably Heists and the more recent The Doomsday Heist.

However, GTA Online had a few words to say about that. The absolutely unexpected runaway success of the multiplayer mode, which included similarly successful microtransactions, clearly caused some resource re-allocation and suddenly Rockstar was releasing one GTA Online DLC after another.