I know the title is a bit vague :\
I remember reading a book with a cat that in the middle of talking would stop to groom himself. I think he talked mostly in riddles and ambiguously (As would befit a cat).
I more specifically remember an instance where a human (I think it was an older woman) was annoyed with the cat since the cat had said a sentence and then wouldn't talk until he brushed all his fur back and back again.
This has been driving me crazy for quite a while...
I can think of two answers, but since you are referring to an older woman, the book you are searching for is The Last unicorn by Peter Beagle. The woman's name is Molly Grue.
Together with the strange wizard Schmendrick and a unicorn transformed into a girl (Amalthea), they brave the castle of old mean king Haggard who has used the Red Bull to capture all the unicorns in the sea.
The cat lives in the castle too and helps them find a way to the Red Bull.
An alternative is Alice and the Chesire Cat from Alice in Wonderland, but she (Alice) is never old when she talks to him.
There is a book called: Mort(e), by Robert Rapino that features a super intelligent cat-- this may the book your looking for!
