Bigger screen? Doubt it.
I doubt any rumors claiming the iPhone will get a larger screen. Remember: Apple created the Retina Display to have exactly double the ppi (pixels per inch) of the previous iPhone models because it made it easy---for themselves and for third-party developers---to update the graphics to take advantage of the new screen.
Moreover, and this is important, it also made it easy for developers to ignore the Retina Display if they so chose---the iPhone used pixel-doubling to scale the existing graphics, and so interface layouts wouldn't suddenly break. If you were an iOS developer, you could get around to supporting the Retina Display whenever you wanted to, but you weren't forced to support it on Day 1. This meant that customers could trust that their apps would work on their new iPhones immediately, and maybe later the apps would look even better. This is the kind of thing that builds trust between customers, developers, and Apple itself, and don't think that Apple doesn't know and value that.
Ok, so suppose Apple gives the iPhone a larger screen. Then there are three possibilities:
1. There are the same number of pixels on the screen, but they're bigger.
2. There are more pixels on the screen, with the same resolution as on the Retina Display.
3. There are more pixels on the screen, with a different ppi than the Retina Display.
Let's take these one at a time.
Same number of pixels on the screen, but they're bigger
The first possibility seems like a bad move, since it would actually decrease the resolution of the display; the ppi would necessarily go down. I can't believe Apple would go this route. The resolution of the Retina Display is best-in-class (or near it)---why would Apple want to lose that edge?
More pixels on the screen, with the same resolution as on the Retina Display
Ok, so suppose there are more pixels on the screen. If the ppi remains the same as on the Retina Display, then the interface layouts of almost every app would break. Developers would have to create whole new interfaces to accommodate the new iPhone, while still maintaining the original interfaces to support older iPhones, and also having to write device-sniffing code to determine which interface to serve. Users with the new iPhone would find that their apps were broken, and they'd have to wait until developers caught up to the new display before they could use them. That's a big headache to dump on your developers and a big rift in user trust, and I can't imagine Apple doing it.
More pixels on the screen, with a different ppi than the Retina Display
On the other hand, if the ppi doesn't remain the same, then what should the new resolution be? In order to avoid breaking interfaces, it doesn't actually need to have double the ppi, it only needs to have double the total number of pixels across the screen in any one direction. Now, the Retina Display has 326 ppi on a 3.5" screen, for a total of about 1141 pixels across the diagonal. A pixel-doubling screen, then, needs a resolution small enough to squeeze 2282 pixels across the diagonal.
So what would be the resolution of such a screen? A 3.7" screen would need a resolution of 617 ppi to fit 2282 pixels across the diagonal, while a 4.0" screen would need a resolution of 571 ppi. Those are monumentally high resolutions, way higher than resolution of the already-best-in-class Retina Display. I have a hard time believing even Apple could make such displays at iPhone-like quantities while keeping iPhone-like prices.
So, long story short: I don't believe any rumors that claim larger screen sizes for the iPhone. It just doesn't seem practical.