The club's American owners are considering restoring the words 'Football Club' to United's current crest and insist they have no plans to sell the club or rename Old Trafford
United were lambasted by fans when they removed the words from their 43-year-old crest as part of a redesign in 1998.
And the club's executive vice chairman has revealed the American owners have reservations about the current badge, which was launched seven years before they bought the club.
"I didn’t like that change of badge," said Woodward. "Joel [Glazer] didn’t like that change. We will look at that and have a think about that. We are a football club, not a business.
"I described it to our staff that we are a 135-year-old club and that’s what you have to remember. We are a football club, a club with a capital C.
"Strapped to that is a commercial business that’s going to fund a lot of the player purchases going forward here and we have to be supportive of both.
"We’ve got to make sure they co-exist together but don’t impact each other and that’s where we are trying to balance it."
Woodward, who has replaced long-time chief executive David Gill, also insisted the Glazers will not rename Old Trafford and have no intention of selling the club, despite its valuation soaring beyond €1.2 billion amid reported interest from bidders in China and Qatar.
"The heritage is not just important it is central to what we are trying to do," he added. "As an example we will not rename Old Trafford, the name is part of the fabric of the club. It means something to our fans.
"They are long-term owners, together with our other shareholders. They first bought the club eight years ago and there won’t be any change for many, many years."