Eccleston is to play brainwashed albino monk Silas, in Ron Howard's adaptation of Dan Brown's best-selling novel.
"As soon as film producers spotted Chris on Doctor Who they knew they had to go for him - he has everything they want," an insider told the newspaper. "He is a very serious and respected actor who always gives a great performance. He would be brilliant as Silas.
"Some big names have already signed up for the film. Chris has now been sent a script and is mulling it over - but he has been told he may have to wear a long white wig."
Christopher recently decided to quit Doctor Who after just one series, in fear of being typecast.
Filming of The Da Vinci Code will begin in June for a May 2006 release.