The Rams cut 17 players as they try to trim their roster to 53 players by Saturday's 4 p.m. ET deadline, and Sam was not among them, sources said.
The team has four additional cuts to go before the deadline. ESPN.com previously reported the number as five, but wideout Stedman Bailey, who is expected to make the team, is suspended for the first four games of the season because of a violation of the league's policy on performance-enhancing substances and will not count on the initial 53-man roster.
News that Sam survived a round of cuts Friday was first reported by USA Today.
Rookie tackle Mitchell Van Dyk, who, like Sam, was a seventh-round pick (Portland State), also was cut, sources said.
Sam and the Rams closed their preseason with a 14-13 loss to the Miami Dolphins on Thursday night.
Sam led all Rams with six tackles while playing defensive end. He is in a competition with fellow rookie Ethan Westbrooks for one of the final roster spots on the team.
After the game, Sam was asked how he felt with cuts looming.
"You know what, it's not going to be like the draft," he said. "I'm very confident that I'm going to sleep really well tonight, and I'm very confident I'm going to be on a team, the Rams or any other team in the NFL."
Information from ESPN.com Rams reporter Nick Wagoner was used in this report.