Although he doesn't feature heavily in the plans of boss Massimiliano Allegri, the veteran has opted to remain at San Siro.
"I've decided to stay," the former Juventus forward, who moved to San Siro in 2001, told Milan Channel. "It was difficult for me to leave the world of Milan in the space of a few hours.
"I've received a lot of offers over the last few days and I thank everyone because it is nice to be wanted at the age of 38.
"I want to thank Siena in particular, their President and their directors as they did the impossible to try to sign me."