The most common and most likely answer to this crossword clue is the 8 letter word DROOLING
I've seen this crossword clue in The Guardian
D
R
O
O
L
I
N
G
More clues leading to the result DROOLING
Buddy explains!

The straight part
We know that "Slobbering" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case slobbering = drooling.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 DROOLING mean?
DROOLING verb- To secrete saliva, especially in anticipation of food.
- To secrete any substance in a similar way.
- To react to something with uncontrollable desire.
- To talk nonsense; drivel.
- The act of one who drools.