The defender has just over 18 months to run on his current deal and the French champions want to tie him down to fresh terms.
But the 32-year-old’s agent, Paulo Tonietto, has now revealed that the centre-back will not pen an extension until he is assured of Champions League football next season.
“A contract extension with PSG? For the moment, everything is on hold,” Tonietto told Calciomercato.
“We are waiting for December to see how the club is doing. If PSG fails to qualify for the next Champions League, Thiago Silva will certainly not be signing an extension.
“The market? There are a lot of clubs that are interested in him.”
Silva’s decision to stall contract talks is likely to interest Chelsea, Liverpool and United – who have all been linked with the Brazilian in the past.