The person spoke on the condition of anonymity Thursday because the NFL isn't expected to announce the suspension until Friday.
Enemkpali will be suspended without pay for violating the league's personal conduct policy following the altercation that took place in the Jets locker room on Aug. 11.
A second-year player, Enemkpali was immediately released and claimed by the Bills a day later. He appeared in three Bills preseason games before being cut on Sept. 4. Buffalo then signed him to its practice squad on Monday.
Smith is expected to miss at least the first four games of the season recovering from the injury. He has no plans to file charges against Enemkpali.
Enemkpali suspended four games for punching Smith
ESPN Bills reporter Mike Rodak discusses the news that IK Enemkpali will be suspended for the first four games of the season for punching Geno Smith and what that means for the Bills.