The most common and most likely answer to this crossword clue is the 9 letter word MONEYBAGS
I've seen this crossword clue in The Daily Telegraph
M
O
N
E
Y
B
A
G
S
Buddy explains!

The straight part
We know that "Fat cats perhaps" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case fat cats perhaps = moneybags.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does MONEYBAGS mean?
MONEYBAGS noun- A bag, normally with a drawstring, used for holding money.
- (in the plural) A wealthy person.
- A wealthy person.