If you're correct about everything in your question except the fact that the animals are cats, then you might be thinking of "Into Your Tent I'll Creep" (1957) by Eric Frank Russell.
The alien discovers he is telepathic, but he can't hear other aliens, or even humans, but he can hear dogs:
"We are talking at cross-purposes," Morfad interrupted. "Whether I do or do not overhear Terran thoughts depends upon what one means by Terrans."
"Look," said Haraka, "whose thoughts do you hear?"
Steeling himself, Morfad said flatly, "Those of Terran dogs."
"Dogs?" Haraka lay back and stared at him. "Dogs? Are you serious?"
The telepath has read that the dogs a basically controlling humankind:
"Quote: the supreme test of intelligence is the ability to live as one pleases without working," recited Morfad. "Quote: the art of retribution is that of concealing it beyond all suspicion. Quote: the sharpest, most subtle, most effective weapon in the cosmos is flattery."
"Quote: if a thing can think it likes to think that it is God — treat it as God and it becomes your willing slave."
A breeding pair of dogs are offered as a gift:
"Now see here," declaimed Haraka, openly irritated, "we Altairans invented and constructed ships capable of roaming the spaces between the stars. The Terrans have done the same. Terran dogs have not done it and won't do it in the next million years. When one dog has the brains and ability to get to another planet I'll eat my cap."
"You can do that right now," Morfad suggested. "We have two dogs on board."
You can read the story in its entirety in the September 1957 issue of Astounding at the Internet Archive.
If you read this in a collection in the 1980s, it's likely you read The Best of Eric Frank Russell, a collection I once borrowed and would like to find a copy of again.