The Chiefs went 4-12 in 2009, but ended the season on a solid note by defeating division-rival Denver.
Haley and Weis worked together as assistants with the New York Jets more than a decade ago.
"Charlie is a friend of mine," Haley told the newspaper. "We shared three years together [with the Jets] in a room not even able to have two full-sized desks there. Charlie is a guy that I have a great amount of respect for as a coach."
After a successful run as offensive coordinator of the New England Patriots, Weis was hired to lead Notre Dame in 2005. After his team went 6-6 this season, he was replaced by Cincinnati's Brian Kelly.
Weis had a 35-27 record in five seasons with the Fighting Irish.