Brackett, a pending unrestricted free agent, is considered a priority for the organization, and the sides could have something done before the linebacker is scheduled to hit the open market March 5.
"Gary has expressed his great desire to retire a Colt," Brackett's agent, Brian Mackler, told the Indianapolis Star on Friday. "I'm going to do my best to honor his wishes and (team president) Bill (Polian) and I are going to continue to talk."
Brackett, a seven-year veteran, has topped the 100-tackle mark three times in his NFL career and has finished with 99 stops in each of the past two seasons. The former undrafted free agent out of Rutgers is a leader on the Colts' defense.
"When you have a situation with Gary's presence in the locker room, what he means to the community, that he's been fortunate to play in two Super Bowls, won a ton of games, it's a great opportunity, a great place for Gary to finish," Mackler told the Star. "But it's really up to Bill and I to get this thing done."