The French midfielder met Sir Alex Ferguson on two occasions when he was coming to the end of a one-year stint in Spain with Barcelona in 2001.
However, the 41-year-old ended up returning to the capital with Chelsea.
"I did make a wrong choice," Petit told Goals on Sunday. "I was talking with my wife at that time and she wanted to come back and live in London. When I think about that I think I made a mistake.
"In my heart I wanted to go to Manchester United. I met Sir Alex Ferguson twice at Barcelona and he wanted me to sign for Manchester. I made the wrong decision."
Petit went on to bring an end to his career in 2004.