Vlahovic was wanted by the Gunners during the winter transfer window before completing a switch to Juventus.
The striker was one of the most coveted talents in European football after firing in 17 goals in 21 Serie A games for Fiorentina in the first half of the season.
The 22-year-old revealed that he always had his sights set on joining Juve, despite Arsenal pushing for his signature.
"Maybe my agent knows [about Arsenal's offer] but I never talked to anyone about it," Vlahovic told Icon, as reported by The Telegraph.
"I just had one club in my mind because Juventus is Juventus. There is nothing else to say. And now I feel honoured to be given this jersey. It's incredible every time I put it on.
"I definitely identify with their DNA. The Juventus personality coincides with my personality. When you come here you never give up, you fight all the time, you make the sacrifices. This was definitely what I was looking for."
Vlahovic had a solid start for the Italian giants, netting nine times in 21 games, and there is plenty of potential to unlock.
He has been compared to the likes of Zlatan Ibrahimovic, partly due to their similar stature.
The striker, though, is not interested in those comparisons at the current stage of his career.
He said: "Comparing players with great champions who have scored 400, 500 goals in their careers, who have won 20 or 30 titles, is probably a little unfair!
"It doesn't annoy me but it's also true that when those types of comparison are made and then you make one or two mistakes and the expectations have been hyped then you get critiqued. We all have the right to make mistakes; we are all human. I want to have my own career."
Vlahovic also talked about the sports stars, outside of football who inspired him including compatriot Novak Djokovic.
"He's from Serbia and he's definitely number one so I have always admired him," he said.
"He's a great champion. I want to find out more about how he has done certain things. He is so good for mental strength: how he deals with certain problems and how he can play seven matches in a row and overcome seven obstacles [to win a Grand Slam].
"When you believe in yourself, when you are confident, nothing else will destabilise you. You need to have this kind of mental strength. And also when something goes wrong it will definitely help you face problems. I am not really trained to have it. I think it's something that comes with your character, that is really a part of you."