game of thrones - Who are the 3 men who would have a chance against Jaime Lannister in a sword fight?

In Game of Thrones season 2, episode 8, "The Prince of Winterfell" , Jaime Lannister says to Brienne:

There are three men in the kingdoms who might have a chance against me [in a sword fight]

Who are those three people?

I don't believe this quote, or any variation, appears in the books. There was this quote from A Storm of Swords when he is fighting Brienne:

She is stronger than I am.

The realization chilled him. Robert had been stronger than him, to be sure. The White Bull Gerold Hightower as well, in his heyday, and Ser Arthur Dayne. Amongst the living, Greatjon Umber was stronger, Strongboar of Crakehall most likely, both Cleganes for a certainty. The Mountain’s strength was like nothing human. It did not matter. With speed and skill, Jaime could beat them all.

So in the books it suggest that Jaime can beat anyone, though he is only referring to people of great strength, not necessarily of great skill (somebody such as Barristan Selmy, who is not considered to be exceptionally strong but is exceptionally skillful, may be able to beat him).

Is there any canon evidence to suggest who these three people may be?

I won't accept any purely speculative answers. However if there is no direct canon quote answering the question (which I believe to be the case) I will consider answers that are strongly inferred from canonical sources (such as a canon quote saying X is the greatest fighter in the kingdom, for example).

Answer

I'm going to have to agree with the answer they gave when this question was posed on the Movies & TV: there's no way to tell. Jaime never says who the three men are, and without the benefit of his internal monologue, we'll never know for sure. The only person Jaime had ever fought at this point in the show is Ned, who is already dead.

But if we had to make a guess based on the books, I can think of a few possibilities. It's possible the screenwriter had based the line off of the section you quoted above. Of the four men who are stronger than Jaime AND currently alive, three have been depicted in the show: Greatjon Umber and the Cleganes.

Another possibility is that there are three people who are confirmed in the books to have beaten Jaime Lannister in a tourney match: Loras Tyrell on Joffrey's nameday, Jorah Mormount after the Greyjoy Rebellion, and Sandor Clegane in celebration of Ned being named Hand of the King. The only problem with this interpretation is that Mormount is not "in the kingdoms."

Another interpretation might be that Jaime is thinking of people who have beaten him, broadly speaking. In that case, Jorah Mormount could be replaced with Robb Stark, who outsmarted and captured him earlier in the war.

I guess it's worth noting that any way you slice it, Sandor Clegane makes the cut. Good for him!