Calhanoglu watched on as Inter lifted the Serie A title in the 2020-2021 season, when he was playing for fierce rival Milan.
The Turkey international switched city allegiances by joining Inter for the next campaign, which finished with Milan winning the Scudetto and ending a 1,976-day wait for a trophy.
That also marked the first time that Inter and Milan finished in Serie A's top two in consecutive seasons, but Calhanoglu says Simone Inzaghi's side is far stronger than its neighbour.
"Inter are a much stronger team than Milan. We lost a derby that suddenly changed in the 75th minute after [Ivan] Perisic and I were substituted," the midfielder told Tivibu Spor. "We were leading 1-0, then we lost 2-1. The coach [Inzaghi] also contributed to that defeat, I told him. In the cup, however, we beat them 3-0. The team is very ambitious."
Ibrahimovic could be seen smoking a cigar at Milan's title celebrations, where he took the microphone and told supporters: "Hey, send a message to Hakan."
Calhanoglu insists he would not have behaved like Ibrahimovic, questioning his actions at 40 years old.
"He's a 40 year-old man, I wouldn't do a thing like that if I was that age. He's not 18. He likes to be the centre of attention," he said. "This year he didn't contribute to the Scudetto, he hardly ever played. But he does everything to attract the attention of the fans.
"I don't care at all. It's not right because he's someone who always calls me when I'm in Milan, who wants to go out for dinner and ride a motorcycle with me.
"I respected him. He also wrote about me in his book, he had to write these things or his book would be empty. I won't answer him, it's better not to answer."