Podolski joined the Nerazzurri for the rest of the season having failed to establish himself as a regular starter at the Emirates Stadium since arriving from Koln in 2012, scoring 19 goals in just 60 appearances.
The 29-year-old alleged in an interview with the Sun that Wenger declined to even say goodbye to him before he swapped London for Milan, but the Arsenal boss insists the reality was very different.
"I deny it completely," Wenger told reporters. "We spoke many times. I had many conversations with him. Without my agreement, he couldn't go on loan."
Podolski insisted he remains a Gunner at heart but did not hide his disappointment at what he deemed a lack of respect from Wenger.
"He said nothing to me," Podolski told the Sun. "He did not call me or say goodbye.
"I don't need flowers or a kiss from him. But it is about respect, about saying goodbye. For me respect is important. Maybe he had other problems with me.
"I did everything for the club I possibly could have. I don't believe I did anything wrong. I did not get drunk in a club.
"I wish all of Arsenal and their amazing fans the very best for this season and I see myself as a Gunner. Nothing from him to me, though, but that is his way."