Asked directly about Hasselbeck's future with the franchise during his weekly news conference, Carroll said the team would like to do "everything we can" to have the quarterback return for an 11th season with the franchise.
"We don't know the timelines or how that's going to work out, and all that kind of stuff, but that's a big issue for us that we're looking forward to," Carroll said. "He's had a terrific run for us, and we want to see what we can do to keep that going."
Hasselbeck signed his current contract before the start of the 2005 season and followed that by leading Seattle to its only Super Bowl appearance. The deal expires at the end of this season.
"That's the first I've heard of that. I didn't know he said that," Hasselbeck told Chicago reporters during a conference call Wednesday when informed of Carroll's comments. "We've had good communication all year long."
Hasselbeck added that he wants to play on a winning team and one that's "headed in the right direction."
"That's kind of been our goal here," he said. "If we can get that done here and I can be a part of it, that'd be awesome. If not, I understand."
Hasselbeck's first season with Carroll has featured a series of ups and downs, with the quarterback being booed off the field less than a month ago, countered by the highs of last Saturday's 41-36 upset of the New Orleans Saints to open the NFC playoffs.
Blog: Carroll answers the call
It was a stark contrast to Hasselbeck's previous start at home, in Week 15 against the Atlanta Falcons, when he was booed off the field and eventually replaced in the third quarter by backup Charlie Whitehurst. Whitehurst also started the season finale against the St. Louis Rams and led the Seahawks to a 16-6 victory that clinched the NFC West title and a playoff spot.
Hasselbeck walked off the field Saturday to rousing cheers with his daughters at his side and his son, Henry, propped up on his shoulders.
"It was a great experience winning the game and then having them down on the field was special," he said.
Copyright 2011 by The Associated Press