The Italy international has revealed that the Rossoneri did make an approach for his services but that he wants to finish his career at the Friuli
It was reported last month that the Rossoneri were considering making a move for the prolific striker and the Italy international has now revealed that contact was made.
"It's the truth," Di Natale told reporters at a press conference on Tuesday. "However, I'd never leave Udine, even if Real Madrid came knocking. I want to finish my career here and still score a lot more goals.
"I want to get to 150 goals with Udinese; that would be of enormous satisfaction to me. But what matters most are the team's results."
Meanwhile, Di Natale admitted that he is looking forward to linking up with Luis Muriel this season, with the Colombian attacker having returned to the Zebrette after a year out on loan in Puglia.
"He had a great season with Lecce and he has lots of quality," the veteran striker enthused. "But he needs work.
"He is young and in one or two years he could be like [Alexis] Sanchez. He arrived in training camp with a few extra pounds, but he is young and can only get better."
The 34-year-old Di Natale, who has 42 Azzurri caps to his name, joined Udinese from Empoli in 2004.