Perisic joined Bayern on a season-long loan from Inter in August and the German side have the option to make the deal permanent at the end of the campaign.
The 30-year-old's career could have taken a different direction two years ago, however, as United tried to lure him away from the Serie A side, only for him to reject the offer.
But Perisic says he was tempted to move to Old Trafford when he spoke to coach Jose Mourinho on the phone and that it was painful to knock him back.
“How close was I going there? Very close,” he told The Athletic . “It was an amazing thing for me when Jose called me. It was difficult to say no to him. In fact, I really, really wanted to join him and play for United.
"It was a dream of mine to play in all the big leagues. But it didn’t happen. It was painful for me. But I don’t want to go into the details. I only found out myself the real reasons two years later.”
Bayern initially wanted to sign Leroy Sane in the summer after losing star wingers Franck Ribery and Arjen Robben, but they were forced to look elsewhere after the Manchester City star suffered an injury.
Perisic was signed as the alternative and has already scored two goals in his three Bundesliga appearances for Bayern, who sit top of the German top flight.
And, although the ex-Wolfsburg and Borussia Dortmund player knows he was not the club's first choice, he is confident he can keep impressing at the Allianz Arena and earn a long-term deal with Niko Kovac's team.
“We are talking about Bayern, one of the best five clubs in the world," he said. "They always have three, four or five possibilities for every position they’re interested in. I was not the first.
"It happened very quickly. Everyone knows the story: after Sane got injured, the club contacted Inter and then my agent. I thought about it with my family for one night. Then I agreed.
“I believe in myself enough to think that I can convince the club to make my move permanent. That’s my wish. I will do anything I can to make it happen.”