If Sam passes his physical, the Cowboys intend to sign him to their practice squad, the source said.
"It's been a roller coaster this past week but I'm happy where I'm at now," Sam told MailOnline. "I'm just looking forward to being a Cowboy, my focus is on making the team."
Sam, who is seeking to become the first openly gay athlete to play in the NFL, was cut by the St. Louis Rams on Saturday.
"It has all happened so quickly, but it's exciting, I just wanna get back to playing football you know," Sam said. "I haven't had chance to speak to any of my family yet, not even my mom, but I will. I never followed the Cowboys growing up because I never had a team. I am a fan of defenses and Dallas need some help, that's why I'm going."
The Rams spent a seventh-round draft pick, No. 249 overall, on Sam in May's draft. He put together a solid preseason performance, coming up with 11 tackles and three sacks. In Thursday night's preseason finale against Miami, Sam finished his preseason work with a team-high six tackles.
Sam cleared waivers Sunday and is free to sign with any team.
The Rams finalized their 10-player practice squad on Monday, and it did not include Sam.
Coach Jeff Fisher had suggested that a lack of bodies at positions with little depth could leave the defensive end on the outside looking in when the team added to that unit.
The Cowboys announced Tuesday that rookie defensive end DeMarcus Lawrence, their second-round pick, has been placed on injured reserve with a designated to return tag. That means Lawrence, who is recovering from surgery to repair a broken foot suffered early in training camp, is ineligible to practice for six weeks and must sit out the first eight games. The Cowboys signed defensive end Jack Crawford, a two-year veteran cut last week by the Oakland Raiders, to take Lawrence's place on the roster.
The Cowboys also signed offensive tackle John Wetzel and defensive back Jemea Thomas, who were both cut by Dallas after making the initial 53-man roster, to the practice squad. The Cowboys now have 10 players on the practice squad, meaning they would have to release one to make room for Sam.
ESPN.com Rams reporter Nick Wagoner and ESPNDallas.com's Tim MacMahon contributed to this report.