The plasterer was the sole British applicant for the 1988 Winter Olympics ski-jumping competition and became the first competitor to represent Great Britain in the sport.
He became a national treasure despite his lack of success - finishing last in both of his events.
In 2007, Coogan was signed up to tackle the role of Edwards in a film depicting the comical athlete's Olympic journey.
But British newspaper the Sunday Mirror reports Grint will now take over from the Night At the Museum star.
The movie, directed by Declan Lowney, is scheduled to go into production later this year (09).