The former vice-chairman of Arsenal said he had heard no rumours about the problem while at the FA.
Speaking on the fringes of a Soccerex Asian Forum in Doha, Dein, also a former vice-chairman of Arsenal and the man responsible for appointing Arsene Wenger as manager, said he had heard no rumours about the problem while at the FA.
"I don't think we have heard the end of it," said Dein.
"Not just in England by the way, it will permeate to other countries, it's bound to, it's bound to."
Since former player Andy Woodward came forward three weeks ago to reveal he was abused by convicted paedophile Barry Bennell during his time at Crewe Alexandra, a wave of allegations has swept through English football.
Fifty-five clubs have reportedly been named to police and 18 police forces are investigating claims.
Some 20 former players have spoken out about abuse.
Earlier this week, the FA said it would launch an investigation into the allegations.
On Monday, an independent body set up by former footballers to help victims of child abuse in football, claimed the issue was a "global" problem.