It has been reported by Sky Sports that Silva will undergo a Chelsea medical in Milan on Thursday before signing a 12-month contract, although he could stay at the Premier League for another year.
After his medical, the Brazil international central defender will fly to London on Friday before going into a 14-day quarantine as per the rules in England.
This despite French giants and this past seasons Champions League finalists PSG making a late attempt to convince the 35-year-old central defender to sign a new deal.
Silva had been on the books of PSG since 2012, and won the Ligue 1 title seven times.
The former AC Milan defender made 20 starts and one substitute appearance in Ligue 1 and played nine times in the Champions League for PSG during the 2019-20 season.
Chelsea finished fourth in the Premier League table this past season and will play in the Champions League in 2020-21.