The former coach of the Miami Dolphins signed an eight-year deal in 2007 when he took the Crimson Tide job.
The extension must be approved by the board of trustees.
"Coach Saban has impressively led the Alabama football program back to national prominence in a short period of time," Moore said on the school's Web site Saturday. "This contract extension is a clear statement of our mutual commitment to building on the foundation he has established."
In two seasons at Tuscaloosa, Saban is 19-8, including a 12-2 record and the SEC West Division title in 2008.
"The outstanding support from Mal and the athletic department have set the table for us to be successful," Saban said. "We greatly appreciate the time, effort and dedication of everyone involved in out football program."