The Red Devils were tipped to unite the Brazilian duo at Old Trafford, but Ronaldinho's transfer to the Camp Nou saw Sir Alex Ferguson recruit Cristiano Ronaldo for his attack instead.
Speaking to FourFourTwo (h/t Ieuan Ivett for MailOnline), Kleberson explained he had discussed moving to Manchester with Ronaldinho and expected the superstar to become a United player.
"When [Manchester] United's interest in me was confirmed, I was with the national team in France for the FIFA Confederations Cup.
"I can remember it clearly: I was with Ronaldinho and his brother/agent, Assis. He said: 'They want to sign both of us' and I said, 'OK, let's go, then!'
"I was so glad that he would be coming with me.
"I went back to Brazil and kept negotiating with United, but then Ronaldinho fooled me and went to play in the warm weather at Barcelona! He sent me to Manchester."
Kleberson added: "That's a joke between us until today. He knows that he owes me one."
Ronaldinho experienced a golden spell in Spain, winning two La Liga championships and the 2005-06 UEFA Champions League. The legend also picked up the 2005 Ballon d'Or, crowning his reputation as the best player on the planet.
United signed Ronaldo with Kleberson immediately after the Brazilian midfielder had won the 2002 FIFA World Cup in South Korea and Japan. However, Kleberson failed to regain his impressive international form at club level, and the pace of the Premier League appeared too much for him.
Injuries hampered Kleberson's two-year spell in England, and he joined Turkish giants Besiktas in 2005.
Ronaldo's capture saw United create further success as they developed the Portuguese teenager alongside Wayne Rooney.
The winger won three consecutive Premier League titles under Ferguson from 2006 and collected the Champions League and Ballon d'Or during his Red Devils career.