PSG risks losing the Brazil international as he continues to wait for a new contract offer for the Ligue 1 champion, his current deal due to expire at the end of the 2016-2017 season.
The 32-year-old is keen to stay in the French capital, but his agent has made it clear there is plenty of interest in the centre-back's services.
"It is very important for everyone - both for us and for PSG - that everything is clear by December," Tonietto told Le Parisien.
"We can imagine leaving PSG if the club have not made us an offer by then. We already have offers from three or four big teams.
"But Thiago's desire is to stay at PSG. He is feeling very well in Paris, as is his family.
"But it all depends on what the club want."
Thiago Silva joined PSG from AC Milan in 2012 and has made over 160 appearances in all competitions for the Ligue 1 giant since, winning four league titles in the process.