I don't think there's any definitive proof, but my educated guess is that the mooted Animals quad mix was simply a victim of bad timing.
Maybe one of the Pink Floyd experts can chime in, but it's my understanding that the stereo mixing of the album was done at the very tail end of 1976 (or even the very beginning of January 1977 if you believe Wikipedia) and the album was released that month. The band embarked on a 6 month tour almost simultaneously, so you'd imagine preparations and rehearsals for the tour probably started almost as soon as the album was in the can.
From what I can gather, the band's new (at the time) Brittania Row Studios was quad equipped, and I'm sure Columbia would've been more than happy to foot the bill for the quad mix, as they released more than two-dozen pop albums in quad between the beginning of 1976 and the end of April 1977, when their final batch of quad releases (RTF Musicmagic, Isley Bros. Go For Your Guns, and Wild Cherry Electrified Funk). So, Animals is well within that window having been released in January 1977.
I think if Floyd had been a smaller band with less artistic control (or had a less hands-on approach) you probably would've seen them hand the master tapes over to either their engineer (Brian Humphries, who did WYWH) or CBS's in-house guys (Larry Keyes or Don Young) to do a quad mix while they were on tour, but being as they were they probably wanted to have a say in how it was done, and there was no way that could happen until the tour was over. The problem was that by the time the tour was over and Roger Waters had spit on the kid in Montreal, it was July 1977 and CBS's quad program had been dead for 3 months already (not to mention EMI's which I'm pretty sure hadn't had a pop quad release since WYWH in 1975) so the moment of opportunity had passed.
As others have already said upthread, the band didn't seem to have a problem with including the rough-around-the-edges (to say the least) test quad mix of Echoes on the box set, so I'm sure if there was an extant quad mix of Animals they would've included it on this new Blu-Ray, and so you can pretty safely infer that it doesn't exist as a result.