Virgil van Dijk claims he knows nothing of interest from English clubs and is keen to prove himself in the Champions League with Celtic.
QPR loanee Tom Carroll wants to "make it at Tottenham" but is prepared to consider all of his options at the end of the season.
The new deal means the 28-year-old Brazilian is tied to the Ligue 1 club until June 2018, ending the speculation surrounding his future after he was heavily linked with a move to Barcelona earlier this summer.
"We are very proud to have extended with Thiago, an exemplary player both on and off the pitch," club president Nasser Al-Khelaifi said in a statement.
"He symbolises PSG's wish to build one of the most successful teams in Europe in the mean time."
Silva joined PSG in July last year from AC Milan and made 22 appearances in last season's title-winning campaign.