Speaking to the Financial Times today, he said that the "best way for the video games industry to have the talent and the skills it wants is to move into the hot seat itself; to come to the government and say 'we want to put some money into an academy'."
What he called a "school for geeks" would not only target those looking to get into games but those usually left out by traditional academia: "You might have kids who traditionally have quite a difficult time coping with traditional academic subjects but happen to be the most amazing gamers… you have to look very creatively at the kind of educational background you want."
His words came as the government prepares to publish a green paper this spring that will look at all of the UK's creative industries - from video gaming to advertising, music and television - point out that the country's entertainment content-makers are a big part of the economy and underline their position globally.
"They're now recognising that 'actually we're huge, maybe we need to build our own institutional bricks'," the minister added of the games academy. "You see television and films schools but we don't have a video-games school. Why not? Because [the sector] is so new. And yet we're the third largest manufacturer in the world."
Woodward said he was confident that there would be private sector support for the theorised initiative - although he was not pressed further on whether the support would be from developers, publishers, or third party financers.
A number of studios around the world already have links to established universities and colleges, and EA even has its own EA University program, however in the UK there is no such dedicated games academy such as the London Film School, for instance.
Develop will explore Woodward's suggestion and the related issues further in its February issue, which also includes an extensive report into the recruitment and job market for games developers.