The talks in Milan are understood to have gone well, with the 23-year-old defender nearing a move to Stamford Bridge.
Chelsea are thought to be offering €40 million (£36m/$47m) for Rugani's services, while Juventus are holding out for €50m (£45m/$58m).
The two sides should be able to find a compromise over that €10m gap, especially if Chelesa were to offer add-ons to bolster their €40m offer.
The Blues are set to offer Rugani a contract worth €4.5m per season.
Chelsea boss Maurizio Sarri has prioritised the signing of Rugani, whom he managed during the defender's spell at Empoli between 2013 and 2015.
Rugani has been capped seven times by Italy and is highly regarded, but has yet to establish himself as a regular starter with Juve.
Stuck behind veterans like Giorgio Chiellini, Medhi Benatia and Andrea Barzagli, Rugani made just 26 total appearances in 2017-18, six more than he made the previous season.
Following the €100m purchase of Cristiano Ronaldo, the Old Lady are looking to balance their books by selling off multiple players.
In addition to Rugani's likely exit, Juve are also looking to part ways with prolific striker Gonzalo Higuain.