The most common and most likely answer to this crossword clue is the 5 letter word FOODY
I've seen this crossword clue in The Guardian
F
O
O
D
Y
Buddy explains!

The straight part
We know that "one that likes to eat" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case one that likes to eat = foody.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 FOODY mean?
FOODY adjective- Eatable; fit for food or consumption.
- Food-bearing; fertile; fruitful.
- Of, relating to, composed of, or supplying food.