Eifert does not need back surgery at this time, the source said.
He missed Sunday's game against the Green Bay Packers but played in the Bengals' first two games. He did not practice at all last week.
Eifert, 27, was one of the team's top red zone targets in 2015 and had 13 touchdown receptions. He played in only eight games last season due to a combination of back and ankle injuries. He has missed 28 games due to injury in his NFL career and has never completed a full season without injury.
He underwent offseason surgery on his back, which he admitted in July will affect him in some ways for the rest of his career. He was unable to participate in practice during organized team activities but was back for training camp.
The 2013 first-round pick is in the final year of his rookie contract with the Bengals.
ESPN's Katherine Terrell contributed to this report.