Samsung is known to announce the Galaxy Note devices at IFA in Berlin, and they've historically announced the new Note devices there, too. It seems they aren't making any exceptions this time, and they will be announcing the Galaxy Note 3 on September 4 in Berlin, at the IFA 2013 event, too.
Unnamed "industry officials" have confirmed this, and they've also confirmed the previously leaked screen size by @evleaks, who said it's going to be a 5.7-inch screen. There have been other rumors before saying that the screen will be 5.9" or even over 6" large, and Samsung may have experimented with those screen sizes, too, but I think in the end they decided 5.7" is the best compromise between bigger screen real estate and how pocketable it is.
At the same time, the 5.7" size for the Note 3 will still feel like an "upgrade" over last year's Note 2, which has a 5.5" screen. Of course that won't make or break the new Note, and its popularity will depend a lot on other factors, too, and I wonder if after the Galaxy S4 "outrage" over the material and the design, they'll be changing them to something different for the Note 3. But I wouldn't put too much hopes in this, because there's just too small of a window to do all that.
There have been some rumors that it will use a flexible (probably YOUM) display, but nothing has been confirmed about that yet, and it could be that Samsung was just testing it, but it's possible it won't be ready for Note 3's launch. The Note 3 should however come with Qualcomm's S800, at least in US, and now that even the Galaxy S4 is getting LTE-A for some models, the Note 3 will most likely get it, too.
A 1080p display should obviously be expected, too. The lack of 1080p display was actually one of the biggest downsides for the Note 2, because it's such a big device, and the Droid DNA was already being launched back then with 1080p and a significantly smaller screen size, so it was disappointing to see it didn't have 1080p. Samsung tends to use lower resolution than competitors when it uses Super AMOLED screens, because they are more expensive, with the exception of the Galaxy S series, where they try to be as current as possible, even if it costs them more.
The Note 3 will be announced in September, but it will probably take at least a month or two before it will start shipping in US and in other countries.