"I think it will be resolved and he'll be a Giant this year," Mara said Monday. "It's something we can work out. We're already talking to his agent to do something incentive wise with his contract to make him happy."
Umenyiora has said Giants general manager Jerry Reese promised to renegotiate his contract, which will pay the defensive end $7.1 million in base salary over the next two years. The team had given Umenyiora's agent, Tony Agnone, permission to seek a trade, but Reese abruptly rescinded that several days later.
Umenyiora is attending training camp after initially not reporting, but he's not participating in practices because of a knee injury. Giants coach Tom Coughlin called Umenyiora's condition "day to day."
Umenyiora spent part of Monday riding a stationary bike at the team's practice facility. Team officials told the New York Times Sunday that he had been receiving treatment on his left knee.
"We want him on this team," Mara said of Umenyiora. "He belongs here. He's had a great career here. He adds a lot to this team. I always say, the reason we were able to win Super Bowl XLII (in the 2007 season) was that they couldn't block our front. That was the first time all year Tom Brady faced that kind of pressure. That, to me, is the heart of our team. We're hoping we can work it out soon."
Citing a person briefed on the talks, the Star-Ledger reported Monday that the Giants are offering incentives based on the number of sacks Umenyiora gets this season. That source said Umenyiora's camp wants a long-term deal, a trade, or one year cut off Umenyiora's contract so that he'll be a free agent at the end of this season.
Umenyiora started all 16 games last season and led the NFL with 10 forced fumbles. His 11.5 sacks tied Justin Tuck for the team lead.
The Associated Press contributed to this report.