googling "jellicle cats" and "t. s. eliot" yields the phrase
"pollicle dogs and jellicle cats"; continuing the search with this phrase gives:

A defining moment in the series is when Eliot introduces the feline creatures of Old Possum's Book of Practical Cats to the three-year-old Tom. He writes: "I am glad you have a Cat, but I do not believe it is So remarkable a cat as My Cat. My Cat is a Lilliecat Hubvously. What a lilliecat it is. There never was such a Lilliecat. Its Name is JELLYORUM and its one Idea is to be Usefull!! For Instance It Straightens The Pictures - It Does The Grates - Looks Into the Larder To See What's Needed - And Into The Dustbin To See That Nothing's Wasted - And Yet Is So Lillie And Small That It Can Sit On my Ear (Of course I had to draw my Ear rather Bigger than it is to get the Liilicat onto it)."

Just before Tom's fourth birthday, Eliot sends him a verse "Invitation to All Pollicle Dogs & Jellicle Cats To Come To The Birthday Of Thomas Faber", beginning: "Pollicle Dogs and Jellicle Cats!/ Come from your Kennels & Houses & Flats…" (this hitherto unpublished poem was incorporated into the lyrics of the Prologue of Andrew Lloyd-Webber and Trevor Nunn's critically acclaimed musical Cats.

stating that jellicle cats are such and so are probably just as fanciful.