Paolo Tonietto has claimed that a deal for the Brazilian, which is reported to be worth as much as £40 million, is in the works.
"Negotiations have existed between Milan and Paris St Germain," Tonietto told tuttomercatoweb.com. "But I don't know if Milan will sell him.
"Should Milan decide to sell him, it would be the best time for Thiago to change clubs."
Earlier on Tuesday Milan moved to play down talk that they are planning to let their star centre-back leave after three years at the San Siro, with sporting director Ariedo Braida telling Sky Italia: "Be calm, we will not sell Thiago."
However, that has not stopped the 27-year-old being linked with clubs such as Manchester City, Chelsea and Barcelona as well as PSG.
"The top clubs in Europe have expressed to AC Milan an interest in Thiago," Tonietto added. "But almost all of them thought that Milan would never sell him, also because we are talking about one of the most important elements of Milan's squad."