Reportedly close, say, brief statement (7)
I believe the answer is:
summary
'brief statement' is the definition.
'reportedly close say' is the wordplay.
'reportedly' indicates a 'sounds like' (homophone) clue.
'close say' becomes 'summery' (close can mean stuffy or overly hot).
'summery' is a homophone of 'SUMMARY'.
(Other definitions for summary that I've seen before include "Precis, gist" , "Brief" , "Synopsis, outline" , "Immediate" , "Perfunctory" .)