Trey Wingo wonders if the Giants are hoping Odell Beckham Jr. stops giving them reasons to question if he is worth a big payday. (1:57)

ORLANDO, Fla. -- New York Giants co-owner John Mara is not ruling out the possibility of trading receiver Odell Beckham Jr., or withholding a contract extension, in the wake of a viral social media video that was posted earlier this month.

Mara, speaking Sunday to reporters at the NFL owners meeting, said there is a "possibility" that the Giants will let Beckham play in 2018 on the final year of his rookie contract.

Asked if it was possible that Beckham could be on another team's roster when the season begins, Mara said: "I can't answer that one way or the other. We're certainly not shopping him. Again, when you're coming off a season when you're 3-13 and played as poorly as we played, I wouldn't say that anyone is untouchable."

Last week, the Giants traded longtime defensive end Jason Pierre-Paul to the Tampa Bay Buccaneers in a surprising move. On the potential that the Giants could trade Beckham rather than commit to him long term, Mara added: "You always listen to those things, but it's not a scenario that I'd like to see happen."

The latest incident for Beckham is the posting of a seven-second clip to social media that showed Beckham in a bed next to a pizza holding what appears to be some sort of brown cigarette or cigar. There was a woman next to him with a credit card and what looks like a white powdery substance aligned in rows.

Mara said he had not spoken to Beckham about the incident but noted that coach Pat Shurmur met with Beckham last week in California while scouting potential draft picks.

Shurmur told the New York Daily News on Sunday that he had a "great" meeting with Beckham. Under NFL rules, coaches aren't allowed to talk football with players before the start of OTAs. Shurmur told the newspaper that he and Beckham didn't discuss football during their meeting.

"I had an opportunity to visit with Odell and got a chance to get to know him a little better," Shurmur told the newspaper.

Mara said he didn't know "what was in the video exactly" but once again made his disappointment clear.

"I think too often he allows himself to be put in bad situations and needs to use better judgment," Mara said in a stern public rebuke.

"As I've said before," Mara said, "I'm tired of answering questions about Odell's behavior and what the latest incident is. I think he knows what we expect of him, and now it's up to him."

Mara, asked earlier in the day by the New York Post and Newsday whether Beckham's behavior in the video was an indication that he failed to live up to the team's expectations, said, "it wasn't helpful."

The enigmatic wide receiver was suspended for an on-field incident with cornerback Josh Norman in 2015 and has been fined numerous times by the league for his actions and behavior, including last season, when he pretended to urinate on the field like a dog after scoring a touchdown against the Philadelphia Eagles.

Beckham, whose 2017 season ended early because of a broken ankle he suffered against the Los Angeles Chargers in Week 5, is set to play this season on the fifth-year option of his rookie deal worth $8.5 million.

The Giants have previously said they hoped to have him re-signed before he becomes eligible for free agency.

ESPN's Jordan Raanan contributed to this report.