Homer perhaps with good information about Odysseus’s origin (6)
I believe the answer is:
pigeon
'homer perhaps' is the definition.
(homer is a kind of pigeon)
'good information about odysseus's origin' is the wordplay.
'good' becomes 'pi' (I've seen this in other clues).
'information' becomes 'gen' (gen can informally mean information).
'about' is an insertion indicator.
'origin' suggests taking the first letters.
The initial letter of 'odysseus' is 'o'.
'gen' enclosing 'o' is 'geon'.
'pi'+'geon'='PIGEON'
'with' acts as a link.
(Other definitions for pigeon that I've seen before include "Seed-eating bird" , "run, perhaps" , "Common bird, wild and domesticated" , "Bird of towns and woods" , "Epigon (anag.)" .)