The nine-year NFL veteran, who held out for the opening day of training camp, noted that teams don't hesitate to release players after they are injured, or to ask them to take pay cuts when their roles are reduced. Umenyiora also said they should reward players who are being underpaid.
The Giants cut veteran starting offensive linemen Shaun O'Hara and Rich Seubert last week, and they had running back Brandon Jacobs, who last his starting job to Ahmad Bradshaw, rework his contract to take less money.
"It's just frustrating to see how people react to one thing and not the other," Umenyiora said. "Just be fair."
Umenyiora said in an affidavit in an antitrust suit against the league during the lockout that Giants general manager Jerry Reese agreed to redo his contract if he had a good season in 2010. Reese has refused to discuss what he said to Umenyiora.
If the Giants trade Umenyiora, they aren't about to do it for cheap. A league source told NFL Network insider Jason La Canfora on Monday that the Giants are seeking a first-round draft pick in return, although a market might not exist at that price. Receiving a second- or third-round pick is feasible, sources said, and Agnone contacted several teams Monday about the defensive end.
Some teams harbor concerns over Umenyiora's health, but any trade would be pending a physical.
Possible suitors for Umenyiora include the Seattle Seahawks, Baltimore Ravens, New England Patriots and possibly even the Atlanta Falcons, considering how aggressive they have been -- even on the heels of signing free agent Ray Edwards. The Cleveland Browns also are keeping watch over the pass-rush market.
Umenyiora reported to Giants training camp Saturday. He took a physical Sunday but didn't practice with the team. He has attended meetings.
"What really annoys me is the hypocrisy of people clamoring for my head for asking for a new deal or to be traded," Umenyiora wrote in the email to The AP. "Saying I have 2 years left on my deal. These contracts only mean something to us? Where is O'Hara? Where is Seubert? True inspirational football players.
"They were cut after being injured," he said. "They have years left on their deal. Why is Jacobs asked to take a pay cut? He has years left on his deal. The fact is in the business we are in, if you get injured, or they feel like you underperformed, they cut you without hesitation. But if you clearly outplay your contract, and ask for something to be done, you're a bad guy and not a team player. It's ridiculous."
"How does a guy who had one good year (no disrespect to Charles Johnson) sign a deal and make more than both me and Tuck combined?" Umenyiora added in the email. "It's not right. Everyone in this business understands that is exactly what it is. Business. And just like none of us get upset when our teammates are released due to business decisions, the teams also don't get upset when something like this happens."
Tuck said that Umenyiora's holdout and the recent trade talk hasn't been a distraction. He hopes Umenyiora will be a Giant when the season starts.
Losing Umenyiora would hurt though, Tuck said.
"There are not a lot of guys like Osi," Tuck said. "It's not like you can just go and pick up one of those guys off the street, but again as of right now, he's still under contract with the Giants and that's hopefully how it will be for the rest of the year."
The Associated Press contributed to this report.