
I've got a similar situation & I think it's because she's not well (we've had all the possible tests done at the vet & they've found nothing so far).
My cat has started to get clingy but also has a death wish. The labs do not chase the cats & the cats know this but the TT & Spanish given half a chance would chase. The latter live in the kitchen & the cats don't come in the kitchen. The old girl (14) has now started walking around the kitchen. The dogs keep looking at me as if to say "well can we?"
My cat has also lost a huge amount of weight & it was that reason rather than her death wish & clinginess that made me take her to the vets, but as I say, they found nothing. (I'd rather know what I'm dealing with as there is obviously something wrong :-().