And at the start of this month, the FA chairman called for more money generated by the Premier League to filter down the football pyramid.
Neither Scudamore, or any reprehensive from England's top division, currently sit on the 2018 board and Kenyon is keen to see relations thaw in order to help the bid progress.
"Everyone around the table wants English football to progress and that doesn't mean just club football," he added. "It means ultimately getting the World Cup in 2018.
"We have a fantastic product. The structure of the 2018 project is still being finalised and I'm sure there are plenty of opportunities for a broader group to be active in the bid.
"Once this thing gets rolling, it will engage. As I travel round the world, the leagues and the associations are not contradictory and speak in the same vein on issues. This is where we need to concentrate our efforts.
"We should not be shooting ourselves in the foot at critical times like this."
Meanwhile, England manager Fabio Capello has been named as one of six new bid vice-presidents for the bid.
He was named along with Kenyon, former FA chairman Geoff Thompson, Professional Footballers' Association chief executive Gordon Taylor, Tesco chief executive Sir Terry Leahy and Lord Stern of Brentford, formerly chief economist of the World Bank.
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