The sources spoke to The AP on Tuesday on condition of anonymity because the talks are confidential.
"If they're willing to look into the possibility of dealing him, of course we'll listen to them," Fisher said. "We listen to those types of things almost every day.
"This just happens to be a big story because of the circumstances and the situation that arose with the offseason payment and then, of course, with all the drama associated with the offseason conditioning and the conditioning test and everything. Our focus right now is on (Sunday's season opener against) the Raiders."
Redskins quarterback Donovan McNabb also discussed Haynesworth on a radio show and said the team can't win without the lineman.
"He plays a major part on our defense, and everyone knows that," McNabb told ESPN980. "It's just unfortunate what's been going on and how everything has transpired, but that's the game of football, and I think he'll handle it the right way."
ESPN first reported the teams were discussing a possible Haynesworth deal.
Shanahan was hired in January to coach the Redskins, and Haynesworth didn't participate in the team's offseason program while lobbying for a trade because he didn't want to play nose tackle in the new 3-4 defense. Shanahan gave Haynesworth a chance to leave, but the tackle stayed and accepted the bonus in his contract.
Haynesworth skipped a mandatory minicamp and was fined. In training camp, Shanahan required Haynesworth to pass a conditioning test before practicing, which the lineman didn't do until the 10th day of camp. The tackle seemed to be accepting his role in the 3-4 defense by the third preseason game.
Then Shanahan made Haynesworth play almost the entire game Thursday in the preseason finale against the Arizona Cardinals when the regular starters had the night off. Haynesworth played 49 of 55 snaps and was on the field in the final minutes.
His status for Sunday night's opener against the Dallas has been in question, with Shanahan saying only that he will play the best players ready to play.
And the Titans know him well, having drafted Haynesworth in the first round in 2002. They used the franchise tag to keep Haynesworth in 2008 to help keep him focused, and the deal they eventually offered in 2009 was nowhere near what he received from the Redskins during the first hours of free agency.
The former University of Tennessee lineman has 28 career sacks and six forced fumbles in his first eight NFL seasons.
The Associated Press contributed to this report.