PSG was unable to claim a maiden Champions League title as Bundesliga and DFB-Pokal holders Bayern triumphed 1-0 in Lisbon on Sunday to complete a 2019-2020 treble.
Silva signed a contract extension to remain at PSG until the end of their Champions League campaign amid links to Chelsea and Serie A side Fiorentina.
Chelsea is reportedly the favourite to sign PSG star Silva on a free transfer and the 35-year-old defender discussed his future post-match.
"It was my last game in Paris. I am sad," Brazil international Silva said.
"I apologise to the fans. I thank all the fans for their love. I'll come back, with another role, in this club I loved.
"I want to play for another three, four years and play at the World Cup in Qatar."
Silva has enjoyed great success since joining PSG from Milan for a reported €42million in 2012.
The PSG captain has won seven Ligue 1 titles, five Coupe de France crowns, six Coupe de la Ligue trophies and five Trophee des Champions.
Of those honours, six have come during Thomas Tuchel's tenure as head coach in Paris.
Tuchel hailed Silva in his post-match news conference, telling reporters: "Thiago was my captain and it was a pleasure to have a player with quality and personality like him.
"He extended his contract with us for two months. He gave his heart and energy on the pitch, he gave everything to win this Champions League. He deserved to win it.
"We went through some tough times, there were some big disappointments. I'm absolutely proud that he was my captain.
"We're going to talk to the club now, with him, to clarify the situation. No matter what the decision is, he'll still be my player. He's in my heart and it was incredible to play with him."