Genoa want to snap up Zappacosta and have hit the accelerator in a bid to land him quickly.
They are now close to securing him on a season-long loan deal, according to Italian outlet Tutto Mercato.
It is claimed that Zappacosta, who spent last season on loan in Italy with Roma, is set to undergo his medical checks with the club on Friday.
If Zappacosta comes through the medical check with no issues, he will then put pen to paper to a loan contract at the Serie A club.
Genoa finished just one place above the drop zone in Serie A last season and conceded a whopping 73 goals in their 38 league matches.
Zappacosta, 28, saw his stint at Roma interrupted by a serious cruciate ligament injury, restricting his appearances in Serie A for the Giallorossi to just nine.
The full-back has a further two years left to run on his contract at Chelsea.