The seven-second clip posted on social media shows Beckham in a bed next to a pizza holding what appears to be some sort of brown cigarette or cigar. There is a woman next to him with a credit card and what looks like a white powdery substance aligned in rows.
A second video shows what is believed to be the same woman kissing and taping Beckham while he was asleep.
ESPN has been unable to confirm where or when the videos were filmed. The Giants and the NFL acknowledged only that they know of their existence.
"We're aware of the video, but we don't have any comment beyond that," a Giants team spokesman said via email Friday night.
The NFL, through a spokesman, also declined to comment further.
Beckham was in Spain on Friday visiting with soccer superstar and fellow Nike endorser Cristiano Ronaldo. Requests for comment from Beckham's camp have not been returned as of Saturday afternoon.
The video comes at an inopportune time for Beckham, who is looking for a lucrative long-term contract this offseason. He is set to play on the fifth-year option of his rookie deal worth $8.5 million.
The Giants and owner John Mara have said on multiple occasions that Beckham would be a Giant for life and that it was only a matter of when he received a long-term deal. It's unclear at this time whether the videos could factor into the equation.
Marijuana remains banned by the NFL's substance abuse policy. Beckham is not known to have ever failed a test or to have at any point entered the league's substance abuse program.
The Giants still want to see that Beckham has fully recovered from a broken ankle that ruined his 2017 season and were hoping he was past some of the incidents that marred the early part of his career. 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.
Mara said publicly that he was "unhappy" with Beckham after he pretended to urinate on the field like a dog after scoring a touchdown against the Philadelphia Eagles last season. Beckham kept a low profile after that Week 3 incident.
The new Giants brass -- coach Pat Shurmur and general manager Dave Gettleman -- have been open-minded about the top playmaker since their arrivals.
"It's a clean slate," Gettleman said last week at the NFL scouting combine. "I'm not worrying about what happened in the past. You want to know the why. You always have to get to the why. Eventually we'll get to that. If you don't get to the why, you can't figure it out. You can't fix it. So we'll get to the why, and we'll move forward."
Beckham has spent most of the offseason rehabbing and working with his trainer in Los Angeles.
The Giants (3-13) badly missed their top receiver after he fractured his ankle during a Week 5 loss to the Los Angeles Chargers. They finished 31st in the NFL, averaging 15.4 points per game.
Beckham has reached the Pro Bowl and set numerous records in his first three professional seasons.