"There is a lot of talk about my return," Shevchenko said in a television interview published in Corriere dello Sport. "But I am not authorised to say anything more than this: that my links to Milan have always been great.
"Milan gave me a lot, they helped me grow as a player and they helped me win the European Footballer of the Year award and the Champions League.
"I have great memories. Relationships with my team-mates are very important and many of them have remained.
"I thank him for everything he has done for me, he is very close to my heart. He helped me a lot, in many things.
"I miss my friends in Italy, the true ones, and the food, a lot."
Shevchenko has failed to shine at Stamford Bridge since his £30million move in the summer of 2006, although his record of 20 goals in 68 appearances is still respectable.
And another season of disappointment which has seen him rarely feature in Avram Grant's selection could see him call time on his Chelsea career.
"I haven't managed to play much this year," continued Shevchenko. "Whether for physical problems or technical reasons.
"But in the game I have played in I managed to make a small contribution with seven goals.
"The language? I manage to communicate, I manage to speak to my team-mates, but I am very far from perfection."