The Percy Jackson And The Lightning Thief director is said to be considered "the right fit" for the project by Warner Bros producers.
A studio insider told Superman Homepage that an "offer has been sent out to Chris Columbus to direct the 3D Superman reboot for December 2012".
The film will be penned by Jumper writer David Goyer and overseen by Inception's Christopher Nolan.
The source added: "David Goyer really wanted to direct but nobody from either studio think he's good in that arena.
"He's great at coming up with story and ideas, like George Lucas. It's his execution where he's weak, which is why people like Chris and Jonathan Nolan and Guillermo Del Toro have had the best results with his scripts."
Nolan previously revealed that he wanted the movie to have an "incredible story... that audiences can engage with".