The MK Dons chairman believes that the League Two side have nothing to do with the former Premier League side that moved to Milton Keynes in 2004.
Winkelman told the Daily Mail: "The old trophies belong to Wimbledon FC not AFC Wimbledon. They have no claim on that.
"Their history started in 2002 and ours in 2004. AFC aren't in Merton. They've got close but they haven't made it home yet. They may have formed out of the ashes of the club but they aren't them.
"We make no claim to being Wimbledon FC and haven't done for years."
AFC Wimbledon was formed by Wimbledon FC fans who were unhappy with the decision to move the club.
AFC Wimbledon and MK Dons will play each other for the first time in the second round of the FA Cup on December 1.