The controversial winger has become an outcast since he was disciplined by Chelsea after posting offensive messages against the Chinese. Kenedy was sent home from the Blues' pre-season tour of Asia as punishment for his actions.
Benitez has signed Jacob Murphy, Florian Lejeune, Christian Atsu, Javier Manquillo and Mikel Merino in the current transfer window, but has also missed out on some key targets.
The Magpies failed in their attempts to sign Tammy Abraham on loan earlier this summer, and have now turned their attention to Kenedy.
Benitez recently told 'Sky Sports': 'It is very hard because the prices are crazy. We missed some targets at the beginning and we are paying for that, but hopefully we can find some solutions.'
'Sometimes it is not about you want, it is about what you need and what you can afford now.'