Los Angeles Galaxy midfielder Beckham joined AC Milan for two loan spells in total before an injury suffered while at the San Siro ruled the former England captain out of the World Cup.
Bruce, a former team-mate of Beckham’s at Manchester United, said: “Certainly I tried to (sign Beckham) 18 months ago.
“I did try when he went to Milan. Milan or Sunderland or Birmingham or Wigan?
“He just said ‘thanks Brucie, I’m going to Milan’.
“I understand that. Milan and Prada or Sunderland and Primark?”