The Hobbit.

[Remmirath]

Spoiler

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Change? I thought it was Tolkien who said Gandalf joined Thorin specifically to remove strongest piece Sauron could grab in the next war before he had any chance to do so.

Spoiler: Gandalf's motives

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I have certainly not heard that referring to the Ring, and I doubt that it was so said, because it makes little sense with anything presented in either The Lord of the Rings or The Hobbit.

It is already somewhat tied in with Sauron's return, yes, but not with the One Ring except insofar as it was discovered during the events of The Hobbit. During The Hobbit, nobody knew that it was the One. If they did, things would have gone differently, one can assume.

Bilbo stumbled onto the One Ring while in the caverns beneath the Misty Mountains. None of them knew Gollum was there. It took Gandalf and company a while to figure out who Gollum was and what his story was, how he got there, and so forth after the fact. The dwarves weren't even planning on going into caverns in the Misty Mountains at all along the way; they only went there because of a storm and then an unfortunate happening. If all had gone according to plan, they would have continued along the pass without ever entering a cave before they reached the Lonely Mountain.

After Bilbo kept disappearing, and after he was so evasive about the Ring, Gandalf began slowly to be suspicious of it, although at first he simply assumed it was a much lesser ring of power. It wasn't until Bilbo nearly refused to set the Ring aside, much later, that Gandalf became deeply suspicious that it was the One. His suspicions weren't even completely confirmed until he met with Frodo and the Ring was thrown into the fire.

All of that's in the first few chapters of The Fellowship of the Ring.

Now, in the Unfinished Tales, there is a tale which states that Gandalf sponsored and joined the dwarves on their quest to the Lonely Mountain to eliminate Smaug -- because, indeed, Sauron might have been able to use him as a terrible weapon. That may be what you are thinking of, but the strong piece is not in that case the One Ring, rather the dragon. That distinction makes a great deal of difference to the overall flow of events.

Since nobody other than Gandalf was aware of that during The Hobbit, and The Hobbit is all from Bilbo's point of view (well, the book is; they apparently changed that a bit in the adaptation), it doesn't really make sense to me to mention even that much -- it's out-of-character knowledge for nearly the entire cast. None of them should know that Bilbo has the One Ring or that Gollum had it.