Calhanoglu spent four years at AC Milan before becoming a free agent and making the switch to arch-rivals Inter in 2021.
The 28-year-old revealed he made the move to Inter to win the Scudetto but in his first season, the title ended up at back at former club AC Milan, leading to many people poking fun at him.
Ibrahimovic was among the band of people to mock the Turkey international with a barrage of insulting chants aimed towards him during the club's title-winning parade.
"He is a 40-year-old man, not 18, so I wouldn't do that sort of thing at his age. He just likes being the centre of attention," Calhanoglu told Tivibu Spor via football-italia
"He didn't contribute to the Scudetto this season, he barely played, but will do everything to be the focus anyway.
"Besides, he is the one who always calls me up, asks me to go out to dinner or for a motorbike ride. He wrote about me in his book too. He had to write something, or it would've been blank pages. It's best not to bother, honestly."
Despite missing out on the Serie A title, Calhanoglu had plenty of reason to be cheerful having notched up eight goals and providing 13 assists across 46 games in this debut season with Inter.
He didn't finish the season empty handed though as Inter claimed the Coppa Italia, beating Juventus in the final.
On his cross-city move, Calhanoglu said: "It was very difficult, as it was the same city and different colours, but I worked hard and knew this was my opportunity to join the reigning champions of Italy."
"Then when the team I joined didn't win the Scudetto and my old club did, people acted like it was my fault. I am very happy at Inter, though, and the support of the fans is very helpful. I played at Milan for four years, but nobody ever chanted my name in the stands, whereas it happens every time I just warm up for Inter."
Calhanoglu insisted that despite AC Milan's title win, it is Inter who have the strongest squad in Serie A.
"Inter are a much stronger squad than Milan," he added.
"We lost a derby that changed suddenly at the 75th minute after Ivan Perisic and I were substituted. We were leading 1-0 and then lost 2-1, so the coach (Simone Inzaghi) contributed to the defeat and I told him as much.
"In the Coppa Italia semi-final, we beat Milan 3-0."