The Glazers attracted massive criticism following their leveraged buy-out of United in 2005 and some fans were so angered by the Americans' involvement in their club that they formed their own club FC United.
Many supporters who remained loyal were concerned about the fate of the club, fearing the massive debt would be a major handicap in the transfer market and could even raise the potential of United being unable to pay their bills.
But the Glazer family have remained in the background and watched the club win five Premier League titles in eight full seasons, and reach three Champions League finals, one of which they won against Chelsea in 2008.
In an exclusive interview with the club's fanzine 'United We Stand', Woodward said: "I'm sensitive to the general feeling about being fearful about the future of the club under this ownership.
"I think we should explain what the debt means.
"I can understand that [the fans' distrust of the Glazers]. Time will perhaps make them look better owners than some think, especially when they are compared to other owners."
The Glazers launched a successful partial flotation of United in the New York Stock Exchange last year and rumours have persisted of a second such move at some point in the future.
But Woodward expects the family to be around Old Trafford for a long time to come.
"I can't answer for them as I don't know what their intentions are," he said.
"I expect them to be in an ownership position and involved in the club for many years to come."