The report did not cite any sources.
Theoretically, Green Bay could apply the franchise tag to Flynn and then trade him rather than simply letting him become a free agent. That would be allowed by the league, though not encouraged. Teams have until March 5 to use the franchise tag.
"(The Packers) don't do business that way," a league source told the website.
It's prohibited for teams to agree to such a deal before the franchise tag deadline, and one unnamed NFL team executive told the website that would be farther than Thompson is willing to go.
"(Thompson) doesn't bend the rules," the executive said.
The franchise tag for quarterbacks is expected to be valued at $14.4 million for the 2012 season. The Packers would have to maneuver to fit that contract under the salary cap, according to the report, a number which would also be significantly more than the contract of starting quarterback Aaron Rodgers (whose base salary is $8 million).
Flynn, a seventh-round pick in the 2008 NFL Draft, has started just two games in his career, but dazzled in his last significant action, throwing for 480 yards and six touchdowns in a 45-41 victory over the Lions in the Packers' regular-season finale.
It was thought to be more of a possibility to use the tag on Flynn after the Packers reached an agreement with tight end Jermichael Finley on a two-year deal. Finley was scheduled to become a free agent, and the Packers might have been forced to use the tag on him.