Reports in France claim the Brazil international is close to completing a move to the big-spending Ligue 1 side.
According to today's local press, PSG have increased their bid to sign the 27-year-old defender to 50million euros and AC Milan vice-president Adriano Galliani is on his way to Paris to finalise the deal.
However, AC Milan sporting director Ariedo Braida has brushed aside those reports and said to Sky Italia: "Be calm, we will not sell Thiago."
Silva, who is under contract with Milan until June 2016, is also a reported target of Manchester City, Chelsea and Barcelona.
The Brazilian joined Milan in 2009 from Fluminense after previous unsuccessful spells in Europe with FC Porto and Dynamo Moscow.
He made 27 league appearances for Milan last season.