The 32-year-old had the chance to join United in 2003 when it became known that he was to leave Paris Saint-Germain.
However, he opted to sign for Barcelona, where he spent five years before switching to AC Milan.
Discussing his rejection of the Red Devils, Ronaldinho has insisted that their trophy history would have been much different had he been part of the club.
"Yes, that was the only time it has been a real option. If Manchester United had signed me they would have won more European Cups," he told the Daily Mail.
The Atletico Mineiro attacker went on to admit that he does not regret his reluctance to move to the Premier League, although he does rue the fact that he did not play alongside Lionel Messi for longer at the Camp Nou.
"No, because I have played for some of the biggest teams in the world and won everything," he added. "The only regret is not playing more seasons with Lionel Messi.
"He is my good friend. I could see even at a young age he was going to be the best. It was exciting to see this kid who could do things most players can only dream of."
Ronaldinho is part of the Brazil squad that will take on England at Wembley this Wednesday.