The first was at the University of Michigan. On Tuesday, the 2nd of March 1976, he spoke first to a relatively small gathering of students and faculty, and later in the afternoon to a capacity crowd in the Modern Languages Building, where various questions were put to him, some by Professor Donald Yates of the Department of Romance Languages, who wrote up the event as "A Colloquy with Jorge Luis Borges" for The Gyspy Scholar (1976), published by Michigan State University. The colloquy is most easily found in Jorge Luis Borges: Conversations (1998), edited by Richard Burgin. The relevant Tolkien section is as follows.
Question: I’d like him to comment on how that relates to the creative aspects of the reader, that he brings to his reading of Borges. I feel sometimes as though…
Borges: Well, how is the case of Borges different from the case of any other writer? When you are reading a book, if you don’t find your way inside it, then everything is useless. The problem with The Lord of the Rings is you’re left outside the book, no? That has happened to most of us. In that case, that book is not meant for us . . .
Yates: In Chicago, last night and here before and every place else, people come to Borges eager to find out his opinion on Tolkien.
Borges: Well I could never. . . I wish somebody would explain it to me or somehow convey what the book’s good for. Those people say if I like Lewis Carroll, I should like Tolkien. I am very fond of Lewis Carroll, but I am disconcerted by Tolkien.
Yates: Last night you mentioned the difference between Tolkien and Lewis Carroll. You said Lewis Carroll is authentic fantasy and Tolkien is just going on and on and on.
Borges: Maybe I’m being unjust to Tolkien but, yes, I think of him as rambling on and on.
The second instance was in a filmed program, the popular "Firing Line" hosted by William F. Buckley, Jr. It was taped in Buenos Aires on 1 February 1977, and originally broadcast on PBS in the U.S. on 18 February 1977. The full segment, "Borges: South America's Titan," can be viewed here (the Tolkien comments are at timestamp 32.30 and following). Here is a transcription of the segment, slightly edited.
Buckley: Would you go so far as to say that a writer who seeks fame ought not to read books that children can enjoyably read?
Borges: No, no.
Buckley: What about Tolkien, for instance?
Borges: Well, Tolkien--I have found him--I have only found in him utter boredom. I have never got inside his books.
Buckley: When who got inside his books?
Borges: I have never got inside his books. I have always been an outsider. I attempted that "Brotherhood--" Is it "The Brotherhood of the Rings?"
Buckley: Yes. "The Lordship of the Rings," isn't it?
Borges: "The Lordship of the Ring." I don't know. But in any case no rings were awarded me, no. I tried to enjoy him: I did my best. I was in Scotland at the time, doing American theater. Read him, laughed very loudly, but at the same time I felt I got nothing out of the reading. To compare him to Lewis Carroll is blasphemy. I'm so fond of Lewis Carroll.
Here at least Borges admits that he "attempted" The Lord of the Rings. We don't know how far he got. He says he was in Scotland at the time, and it seems Borges was there three times, in the spring of 1963, the late summer of 1964, and the spring of 1971 (after this time in Scotland, Borges went to Oxford where he was awarded an honorary doctorate on 29th April--one wonders if Tolkien attended, or if Tolkien ever read Borges). It could have been on any of these three visits to Scotland that Borges attempted the read Tolkien, for none seem to have any specific association with American theater. And who read Tolkien to him? His sister accompanied him on the first trip; a friend María Esther Vasquez on the second. But it remains unknown who might have read Tolkien to him. And more significant;ly, how much of The Fellowship of the Ring was read to him? I would think not much. Certainly the Prologue and the first few chapters might lead Borges to say he laughed very loudly, but soon after that the tone of the book changes, becoming darker, so it seems that Borges read very little of the book in order to arrive at its humor and his own boredom, such that he (and William F. Buckley Jr.) could not even recall the book's name correctly. Alas.