Jordan Woy, Adams' agent, said he's talked to NFL officials about what happened with his client and Giants defensive end Justin Tuck. Adams pushed Tuck in the back, sending him to the ground. Adams, through his agent, told the league he thought the play was still alive.
"We talked to the Cowboys and the league office," Woy told ESPNDallas.com's Calvin Watkins on Monday. "It's all under review and we told them our side of it."
Coach Wade Phillips said on Monday he talked to Adams at halftime about what happened. Phillips would not reveal specifics of their conversation.
The league declined to speculate on the potential outcome of its review, but Adams at the very least faces a fine and could wind up getting suspended.
"Any altercation of that nature is reviewed for discipline," NFL spokesman Greg Aiello told Watkins.
Adams was given a personal foul penalty though no yardage was marked off against Dallas at the start of the second half.
Giants coach Tom Coughlin said he had spoken with NFL director of officiating Mike Pereira about the play.
"He's already reviewed it with his staff, and they are in the process of discussing it. There was no option given to us [to accept a penalty]. To say the penalty was declined gives the wrong impression," Coughlin said. "That specific aspect of the rule has to be addressed. ... There was no eviction, no penalty, nothing."
Coughlin said he was told there wasn't any option because the penalty happened after the whistle had been blown, after a Giants player in the end zone fielded a missed field goal attempt and stepped out of bounds to end the half.
Adams, who has a history of run-ins with the Giants, caused injury to Tuck in Week 2 when he stuck out his leg and tripped him, causing Tuck to fall to the ground and land on his shoulder.
In that same game, Adams kicked Giants defensive end Osi Umenyiora. He was fined $12,500 for the two fouls.
One week earlier, in Dallas' season opener against Tampa, Adams was fined $5,000 for unnecessary roughness.
After Sunday's game, Tuck lashed out at Adams.
"I laugh at stuff like that," he said. "It just just proves what kind of dirtbag he is."
When asked what happened at the end of the first half, Tuck said, "[The officials] blew the ball dead and I was headed toward the sidelines and pretty much had stopped. And somebody shoved me to the ground from the back and before I could get up he was [engulfed by] our sideline. So I didn't get to sneak any cheap shots in."
In the Cowboys' locker room after the Giants beat Dallas 31-24, Adams had this comment about Tuck: "I ain't talking about him. He's a nobody."
If the NFL opts to suspend Adams, it would inform Dallas of its decision by the end of Tuesday for game-planning purposes. The Cowboys (8-4), who are tied for the NFC East lead, play host to the AFC West-leading Chargers on Sunday.
Information from Calvin Watkins of ESPNDallas.com, ESPN NFL Insider Adam Schefter and The Associated Press was included in this story.