The 32-year-old has been training with the Magpies.
"He played very well in the friendly," said County boss Martin Allen.
"He lives locally, he wants a club and he wants to get back into the Jamaica national team.
"He's been training with us and we might take him out to Italy next week for the Juventus game. He would definitely be a big asset so we will have to see what happens."
Davis played in the top flight with Sheffield United and Derby.