The 34-year-old, who retired from professional football in January, won five Premier League titles, three League Cups and the Champions League with United following his transfer from Spartak Moscow in 2006.
"Rafa Benitez called me and I nearly went there," Vidic told FourFourTwo. "I was interested in going but my English wasn't good and I was struggling to communicate.
"Then Manchester United came. Fergie called me at my apartment and said: 'I watched you play for Serbia against France - I want you here.' United were decisive. Everything was done very quickly, within two days."
Vidic, who got sent off four times while playing against Liverpool, left United in 2014 to join Inter Milan, where he stayed until his retirement.