The league has a search committee working on finding a replacement for Commissioner Paul Tagliabue, who has been held the top spot since 1989. Tagliabue announced his decision to retire in March with a July 31 move-out, but has indicated his willingness to stay on past that date, the Orlando Sentinel reported.
Bush acknowledged Tuesday he discussed the job during a recent meeting with Patrick Rooney Sr., brother of Dan Rooney, who owns the Super Bowl champion Pittsburgh Steelers and co-chairs the NFL's search committee.
However, Bush said he doubted the league would hold out until January for him, the newspaper said.
Among others who have publicly spoken of wanting the job is U.S. Secretary of State Condoleezza Rice, the report said.