Serious enough to swat away an offer from the Washington Redskins that could have netted the Bengals two first-round draft picks, team and league sources said.
Bengals coach Marvin Lewis, who initially denied the team had received offers for Johnson during a Tuesday news conference, confirmed to ESPN that Cincinnati turned down Washington's offer of two picks over the weekend.
"Once I actually read what was reported, I have to be truthful and say that the story is accurate," Lewis told ESPN. "Unfortunately, I didn't read it until after our press conference."
The Redskins offered their first-round pick, No. 21 overall, and a conditional third-rounder in 2009 that could escalate to a first-rounder if Johnson and the Redskins hit certain performance levels, the sources said.
It was not the first time the Redskins approached the Bengals about a deal, but it was the first significant proposal.
Lewis says the disgruntled receiver who wants out of Cincinnati should keep his word and sit out the season.
"I've stated our case with Chad," Lewis said. "He has a contract through 2011. He's stated without an opportunity to go to a different team and a new contract, he wasn't going to play. I think he's a man of his word and says he's not going to play, so don't play."
In addition to getting turned down by the Bengals in their trade proposal for disgruntled Johnson, the Redskins were also rejected this weekend on their trade proposal to the Cardinals for wide receiver Anquan Boldin, sources said.
Boldin is unhappy with his contract after the Cardinals paid big bucks to fellow Arizona wideout Larry Fitzgerald. The Cards say that they won't redo Boldin's deal so he's asked out.
In addition, the Eagles also have inquired to the Cardinals about Boldin and are dangling Lito Sheppard as part of a deal. The Cards are saying no for now.
The Bengals have not only rejected the Redskins, but two other NFC East suitors -- the Dallas Cowboys and Philadelphia Eagles -- have been informed that there has been no change in the team's position that Johnson's contract will remain with the Bengals.
The Bengals have noted to those suitors that Johnson has been the "second-highest paid receiver" in the NFL during the past three years, indignant about suggestions that Johnson also wants a new contract, the sources said.
Trading Johnson also would mean Cincinnati would take an $8 million salary cap hit, but the Bengals are currently $10.5 million under the cap and could restructure other contracts if they wanted to create even more space. Additionally, as one anonymous owner told ESPN.com, "There's nothing wrong with dead money. It's cash already paid and it's cash back in your pocket that you don't have to spend, especially with the [high] amount of everyone's salary cap these days."
Johnson became the epitome of Cincinnati's 7-9 season when he sniped at quarterback Carson Palmer during a loss to New England. Johnson ran the wrong route on a pass play, resulting in a game-turning interception. He initially blamed Palmer for the problem.
Since the end of last season, Johnson has been lobbying for a trade even though he agreed to a long-term deal with the Bengals two years ago. Johnson's contract would pay him $3 million next season and extends through 2010, with a club option for 2011.
Other teams have traded away stars when they started becoming divisive. Bengals owner Mike Brown has a history of refusing to give in to player demands. When running back Corey Dillon tried to force the team to trade him in 2003, the Bengals waited until after the season to send him to New England.
In that case, it was more about getting rid of a player they no longer needed -- Rudi Johnson had emerged as the starter -- than it was about satisfying Dillon.
The Bengals need Johnson in the short term. No. 3 receiver Chris Henry was released after yet another arrest earlier this month, leaving the Bengals with little depth at the position. They might take a receiver high in the draft this weekend.
Last week, when Palmer told reporters that Johnson had assured him he would show up for mandatory team activities, the receiver took issue with him.
On Tuesday, Palmer declined to discuss it further.
"I take it with a grain of salt," said Palmer, who is working out with the team in Cincinnati. "I've moved on and I'm over it. I'm not really going to comment on it much more."
Asked if the two could get along if Johnson stays, Palmer said, "I've always been a forgiving guy, and I hope he's here because he's a good player, and I hope to see him here."
It's been an eventful month for the Bengals. Besides getting rid of Henry, they had linebacker Odell Thurman reinstated by the NFL on Monday. Thurman was suspended for the last two seasons after skipping a drug test and getting arrested for drunken driving.
Lewis said Thurman still must prove he can stay out of trouble.
"There's an opportunity, possibly, if we want, to keep him on the football team and have the opportunity for him to compete for a roster spot," Lewis said. "He's got to do things the right way constantly. That still remains to be seen, whether he can handle that kind of scrutiny day-in and day-out."
Chris Mortensen covers the NFL for ESPN. ESPN.com's James Walker and The Associated Press also contributed to this report.