Suggests this may be around mid-morning (5)
I believe the answer is:
hints
'suggests' is the definition.
('hint' can be a synonym of 'suggest')
'this may be around mid-morning' is the wordplay.
'may be' is an anagram indicator.
'around' is an insertion indicator.
'mid' indicates the central letters.
The middle letter of 'morning' is 'n'.
'this' anagrammed gives 'hits'.
'hits' going around 'n' is 'HINTS'.
(Other definitions for hints that I've seen before include "Slight indications" , "Suggestions" , "Tips" .)