For a team to try to sign him, they have to be willing to give up two first-round draft choices and then have to wait seven days after reaching agreement to see if the Colts will match.
"He wasn't going to go anywhere," Colts president Bill Polian told The Indianapolis Star. "I've had a good talk with his agent [Monday] and we'll continue to talk."
Polian told the newspaper that Freeney is "an integral part of this team and we want to see [that a long-term deal] gets done if at all possible."
In his five-year career, Freeney has 46.5 sacks, including 5.5 sacks during Indianpolis' run to the Super Bowl last season.
He's guaranteed $8,644,000, the average salary of the top five
defensive ends next season.
Michael Smith is a senior writer for ESPN.com. The Associated Press contributed to this report.