Updated: Sep 8, 2020
Chelsea keen to improve squad ahead of next season.
The Brazilian centre-back is now a free agent following PSG's Champions League final 1-0 loss to German giants Bayern Munich on Sunday evening.
Silva, 35, spent eight seasons with the Ligue 1 club PSG after joining from Serie A giants AC Milan in 2012.
If everything goes to plan, Silva will become Frank Lampard's third signing of the summer following the arrivals of Hakim Ziyech and Timo Werner.
Chelsea are eager to strengthen their squad this summer having been banned from recruiting players last summer.
They are also expected to complete deals for Leicester left-back Ben Chilwell and Bayer Leverkusen forward Kai Havertz before the start of the 2020-21 campaign.