The 35-year-old will lead PSG in their first Champions League final on Sunday against Bayern Munich or Lyon.
However, he is out of contract with the Parisians and his representatives are searching for a new team.
Chelsea is reportedly another option for the talismanic Brazilian, who wants to play in the Premier League.
Silva currently earns £1.3m (€1.44m) per month at PSG, but his salary will drop significantly at his next club.
Frank Lampard is in the market for new defenders after conceding 54 goals in the 2019-20 Premier League season.
It remains to be seen if Chelsea reciprocate Thiago Silva’s interest, but he would bring great experience to their backline.