I think Le Carre's claim that he doesn't know is hogwash. Or whitewash. Whatever. Someone who writes and thinks as he does does nothing without intention. The complete answer may be of a larger context due to the fact that Le Carre is of and from and works for British intelligence. Don't let anything fool you that he "resigned" or "retired". Doesn't happen. He just moved into the PR department. Along with his contemporary, Len Deighton.
When you read Le Carre's legend (I'm sorry, life history) you learn his father was a legendary con man who went afoul of the both the law and the "boys". So he was exposed to the "bent" or crooked life early on. A "square John" (John le Carre) is someone who is honest, forthright, and living straight. From Dictionary.com:
An ordinary honest person; a good citizen; a noncriminal person who can be victimized by, and is contemptuously regarded by, criminals.
Substitute the word "Spy" for "Criminals", and I think you have it. I think he is having a little fun with us, because I would say there is certainly nothing "on the square" about his story, role, or story sources. The fact that he will not reveal this tells us it is his private joke and he wants to keep it that way, knowing that to reveal it would expose something he (and his handlers) does not wish known. I'm sure all his buddies in MI-6 get the joke.
I know this appears to be a lot of conjecture; however, the evidence is all there if you read between the lines, know a bit about how intelligence services really work, and know the code. To me, the smoking gun: the solid, unrefutable proof, is given away by the definition of "Square John".