Umenyiora is seeking a new contract or a trade to a team that will give him a raise. He has two years and a total of $8 million remaining on his contract.
"Osi and Jerry had a chance to talk and I think that was something good that came out of that," Coughlin said.
Umenyiora was not available for comment. On Saturday, Umenyiora's camp said the defensive end would not speak to Reese but something changed. It remains to be seen when Umenyiora will return to the field.
The defensive end did undergo his physical but was also scheduled to meet with team Dr. Russell Warren on Sunday afternoon, Coughlin said.
"I doubt that he will be cleared to practice this afternoon, though I'm purely speculating," Coughlin said. "There's been issues over the years, the hip that Osi's had for example."
Umenyiora, who had offseason surgery to repair a hip injury that has lingered for years, was at the Giants late afternoon practice but rode a stationary bike on the side and did not participate. He was joined by center Adam Koets (knee) and wide receiver Ramses Barden (ankle).
In a sworn affidavit as part of the recent Brady vs. NFL players lawsuit during the lockout, Umenyiora said Reese told him in 2008 that if the defensive end were still playing at a high level in two years, he'd reward him with a new contract or trade him to a team that would pay him like a top-five defensive end.
Defensive tackle Chris Canty said Umenyiora has been in a good mood while interacting with teammates. Canty said the Giants "need" Umenyiora this season.
"Osi hasn't been grumpy at all," Canty said. "I know that there's a little bit of a medical issue there as well, so we're going to let that stuff play out as much we can."
Canty added that Umenyiora is "not trying to be a distraction."
"He doesn't want to be," Canty said. "He wants to get back to the business of playing football for the New York Giants. I don't want anyone to misconstrue that. He is a terrific teammate. Football has a business part of it so you got to take care of the business part so you can get to football."
And business has been very good for one defensive end so far in free agency. Canty said he understands why Umenyiora wants a raise, especially in light of Carolina defensive end Charles Johnson agreeing to a contract worth $72 million over six years, including a $30 million signing bonus.
"He is not blind," Canty said. "I am sure ... he is looking at ... as I like to call him, 'Big Bucks' Chuck's numbers. Charles Johnson broke the bank. And that is obviously a going rate for a top-tier pass rusher these days and (Umenyiora) wants to be compensated as such. I don't see anybody that is that much better in the business of pass rushing than he is. So obviously he wants to be compensated as such and I don't blame him."
Ohm Youngmisuk covers the Giants for ESPNNewYork.com.