The Ukraine international has been a long-term target for Napoli sports chief Cristiano Giuntoli.
TMW says talks are set to kick off ahead of the winter market opening next month. An initial loan deal is being considered.
Zinchenko has broken into the City first team this season.
And City boss Pep Guardiola recently said: "Normally he is an attacking midfielder but he can play winger or full back as well.
“Against Wolves, who are first in the Championship and gave us a difficult game, he played full back and did really well.
“He is a talented player, so clear, so clean. The way he plays, his decisions are always perfect. As a young player I hope in the future he will help us.
“He is going to stay for the whole season with us because I have the feeling we are going to use him."