No one was willing to give up the first-round draft pick that the Giants demanded for Umenyiora, but sources said several teams had interest in the veteran defensive end if compensation was a second-day draft pick (Rounds 2 or 3).
Multiple published reports listed the Denver Broncos, Baltimore Ravens, Seattle Seahawks, St. Louis Rams and San Diego Chargers as interested in Umenyiora, who finished last season with 11.5 sacks. However, he's dissatisfied with a contract that will pay him $7.1 million over the remaining two seasons of a six-year, $41 million extension he signed in 2005. Umenyiora is reportedly looking for a six-year deal in excess of $10 million per year.
Unless Giants general manager Jerry Reese changes his mind again, the organization will either negotiate a new agreement with Umenyiora or force him to play under his current contract.
Despite being cleared to practice following offseason hip surgery, Umenyiora has stayed off the practice field but has attended team meetings. He missed the first day of training camp and was fined $30,000.
Umenyiora met with New York's front office Wednesday afternoon, and Reese told him to "take the rest of the day off to clear your head."
Instead, the Star-Ledger reported that Umenyiora stayed, riding a stationary bike, watching drills, and talking to his position coach.
"I was pleased," Coughlin told reporters. "It's a good thing. I'm hoping that's the kind of indication that we're all looking for."
Umenyiora's situation has left his teammates in a quandary, but they continue to maintain confidence they have the right personnel to compensate for any eventuality. The front office also went through one preventive measure Tuesday when former Rams and Washington Redskins pass rusher Andre Carter worked out for the team.
"I don't ever want to get into or discuss anybody else's financial situation," Kiwanuka said. "He's in the building, and obviously we'd love to have him on the field."
Kiwanuka pointed to himself as a walking example of why a player like Umenyiora must find the best deal he can for himself. Kiwanuka missed all but three games last season with a career-threatening neck injury. That became a major factor in team's lack of interest in him during the NFL's condensed free-agent period.
Had he stayed healthy, Kiwanuka could have been a premier free agent.
"But you look on the other side of that coin, and I might not have been playing football," Kiwanuka said. "I'm definitely the example. (Health) is definitely a concern to every player out there. Coaches always say you never know when it's going to be your last snap. So when it comes time for business, that's something you always have to consider."
Linebacker Michael Boley pointed to the presence of second-year pro Jason Pierre-Paul as a quick remedy if Umenyiora continues to stay off the field.
"He's a tremendous athlete," Boley said of the 6-foot-5, 270-pound Pierre-Paul, who finished third on the team last year with 4.5 sacks as a rookie. "To run the way he does at his size, and he's strong at that, he can make a lot of plays for us."
NFL Network insider Jason La Canfora and The Associated Press contributed to this report.