On the other hand, one of the team's biggest needs is at cornerback, and Asomugha is one of the best in the game.
Banner's comments leave the door open for Asomugha speculation - rampant among many NFL fan bases - though he also didn't say anything to indicate that the Eagles would actually pursue the all-pro. He wouldn't comment directly on any individual players because free agency isn't yet open.
Asomugha will probably have many suitors and will command a massive price.
At the moment, free agency is more a theory than reality because of the NFL's uncertain labor situation.
Once the league's shopping period opens, though, the Eagles will have more salary cap room than most teams, and Banner sees a buyers' market with a huge number of free agents potentially available.
"There may be opportunities to get some great players that can make a difference at large salaries. There may be an opportunity to get some guys that are very good players but, because there are so many free agents at once, are very good values, and we're going to try to be in a position to take advantage of" the situation, Banner said in Tuesday's wide-ranging discussion with reporters.
Depending on the rules of the new collective bargaining agreement, up to 500 players might be free.
"If there's truly 500 new free agents, there's no doubt there are going to be some value opportunities. There just aren't that many teams with that much cap room with that many needs to absorb that many players at once," he said.
It's unclear when free agency will happen or who might be available because the labor rules could be rewritten in a new collective bargaining agreement. Banner said the Eagles have planned for a variety of timetables and free agency rules that might come to pass.
Despite the cap room the Eagles have, Banner noted that the team committed a total of at least $19 million to Michael Vick and David Akers by using the franchise and transition tags on those two, and have many of their own free agents to account for.
Banner also spoke about several other issues:
Asked about committing long-term to Vick despite defenses improving against him late last season, Banner made a telling comment that pointed at the Eagles' offensive line play.
"There are other aspects of the unit that [Vick] doesn't control that . . . will be areas that we'll try to get stronger around him," Banner said. "Hiring a different offensive line coach with just a different set of ideas who's a really smart guy may contribute positively to all that."
Injured Eagles rehabilitating during a lockout will not be allowed any contact with the team, though the Eagles are trying to set the players up with independent facilities where they can stay on track. Could the NovaCare medical facility attached to the Eagles' offices and training rooms count as an independent site? Banner said the team was awaiting a ruling on the question.
Players can keep their health insurance if a lockout begins, but they would have to pay for it themselves, he said.
Contact staff writer Jonathan Tamari at 215-854-5214 or firstname.lastname@example.org. Follow him on Twitter at www.twitter.com/JonathanTamari.