Umenyiora visited with a specialist in Atlanta on Thursday to get another opinion on his sore right knee, and Agnone said Umenyiora will not need surgery at this time. Umenyiora has a meniscus issue that can be managed.
"It went well," Agnone said of the meeting with the specialist. "Hope we get him going soon."
When asked if Umenyiora might practice on Monday, Agnone said "probably." The specialist has to consult with Giants team doctor Russell Warren and trainer Ronnie Barnes before figuring out Umenyiora's timetable.
Umenyiora has not practiced since joining the team on July 30. He had surgery on his left knee back in 2008 after he suffered a season-ending injury.
"I hope so," general manager Jerry Reese said of Umenyiora practicing on Monday. "Osi, we expect him to be back in the fold. That situation, I am not going to make any comments, there are still some issues we are trying to resolve but we expect him to be back."
Umenyiora performed some individual pass-rushing drills on the side for the first time during a practice on Wednesday and looked explosive.
Umenyiora has been in a contract standoff with the Giants. He wants a new deal or to be traded and has a total of $7.1 million remaining in base salary on the final two years of his deal.
"I'm trying to not make any public comments about any of that right now," Umenyiora said in an email to the Associated Press. "No real progress as far as the contract goes."
The Giants had dialogue with Umenyiora's camp last week about adding incentives to his contract, which also include sacks incentives. However, Umenyiora countered by asking that the final year of his contract be taken off so that he can play this season and then become a free agent.
Agnone did not want to comment about negotiations between the Giants and the defensive end over his contract. However, if Umenyiora returns to play, he may do so with some incentives added to his contract, according to a source.
Ohm Youngmisuk covers the Giants for ESPNNewYork.com.