The Chicago Tribune, citing unnamed league sources, said the Bears apparently have decided to cut their losses with McNown, their 1999 first-round draft pick.
The Sun-Times reported Sunday that word around the league is that McNown is officially on the trading block and the Bears are entertaining offers if not actively shopping the former UCLA star. The Bears' asking price is believed to be a conditional draft choice.
"I don't really know anything about that," McNown told the Sun-Times. "All I can say is that I am a Bear and I'm competing for the starting job right now, and leave it at that."
McNown completed four of eight passes for 32 yards in a 27-24 preseason loss to the Tennessee Titans on Saturday night.
McNown could be in jeopardy of falling to No. 3 on the depth chart behind starter Shane Matthews and Jim Miller, who is expected to return from a strained hamstring and is a candidate for the starting job. McNown also has been outplayed in two exhibition games by free agent Danny Wuerffel.
Bears general manager Jerry Angelo did not comment on any trade discussions centered on McNown, but did say the team is always looking to improve its roster.
Releasing McNown would cost the Bears approximately $3 million against the salary cap, meaning the team would need to create space through other deals.
The Tribune cited team sources as saying the Bears have spoken to various players about restructuring their contracts. They also are looking to sign defensive end Bryan Robinson to a long-term deal that would reduce the $4.177 million salary-cap hit that comes with his transition tag.
McNown has gone 3-12 as a starter since 1999, including 1-8 last season.