The Brazil international appeared bound for the Parc des Princes after the Qatari-owned Ligue 1 outfit offered €46 million for his services. However, Berlusconi changed his mind over the deal and Thiago Silva now looks set to remain at San Siro along with another rumoured PSG target, Zlatan Ibrahimovic.
"It was a big decision and president Silvio Berlusconi gave a huge gift to the team and fans," Allegri told Sky Sport Italia.
"Ibrahimovic will also stay. He had a strong season, scoring 28 goals. The club decided not to dismantle the squad and will keep the foundations of the team intact.
"The side is almost complete, but the market is open until August 31 and anything can still happen."
Thiago Silva is now being tipped to sign an improved contract with the club he joined from Fluminense in 2009.