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).