Galloway has missed all of training camp as he seeks to renegotiate and extend a contract he signed in 1995.
The Seahawks are offering Galloway a seven-year, $35 million deal, with a $7 million signing bonus. Galloway wants a five-year, $24 million contract, with a $9 million signing bonus.
The Seahawks are depleted by injuries in the receiving corps. But team officials declined to comment on the prospect of Galloway missing the season.
New Seahawks coach Mike Holmgren, who talked with Galloway this week, is fining the receiver $5,000 a day for missing training camp at Eastern Washington University.
"I said 'We want you here, but this is our offer,'" Holmgren said. "It's a fair offer. It makes him the second-highest-paid receiver in all of football."
Antonio Freeman of Green Bay last week signed a seven-year deal worth $42 million, including a $10 million signing bonus.
"We've tried to get hold of his agent since I've talked to Joey. But he won't return our calls now," said Holmgren, who is also general manager and vice president of football operations.
Galloway's agent, Eric Metz, said Wednesday that money isn't the main issue for the receiver.
"Joey doesn't want to be the highest-paid receiver in the NFL," Metz said. "He just wants a fair deal."
Galloway caught 65 passes for 1,047 yards and 10 touchdowns last year in his fourth season with Seattle.
Meanwhile, a source who declined to be identified said the star receiver is willing to sit out the entire season if necessary.
"Joey didn't want to go public on the issue," the source said. "He tries to handle himself with dignity and class. The team is trying to railroad him along."
Galloway, from Ohio State, is working out in Columbus, Ohio, in case the two sides can reach agreement.
"If the Seahawks want Joey to just return punts and still say they'll go to the Super Bowl, he'll do it," the source said.
The Seahawks have not made the playoffs since 1988.
If Galloway does not sign a contract, friends will try to find him broadcasting work this season, the source said.
The Seahawks play their third preseason game Saturday, against Arizona. If he doesn't sign a deal soon, Galloway could miss the Sept. 12 season opener against Detroit, Holmgren said.
"It's getting to that point right now," Holmgren said. "Regardless of how good you are, you need at least a week of practie before you can get on the field."
The Seahawks got a scare in practice Wednesday when receiver Sean Dawkins injured his finger during the morning practice. He returned to the afternoon practice wearing a splint.
Starting receiver Michael Pritchard is out for two to three weeks recovering from knee surgery.
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