Coach Norv Turner had said he would determine Tomlinson's status later in the week, but the newspaper said "no one in the Chargers organization truly expects" Tomlinson to play in the AFC divisional playoff game Sunday.
Sources indicated it's likely Tomlinson will miss the rest of the post-season, the Union-Tribune said.
Tomlinson sat out the second half of San Diego's 23-17 overtime wild-card win over the Indianapolis Colts Saturday because of a groin injury.
Turner said the coaching staff determined that Tomlinson was not 100 percent in the game, in which he scored a touchdown and gained 25 yards in five carries, so he did not play in the second half.
"The injury that he has is not any worse," Turner said. "I think ... he was pretty sore around that area from probably compensating for the injury. It was obvious once he got going, to him and us, that he would not be able to play the way that he'd like to."
The Steelers and Chargers will clash in a 4:45 p.m. game at Pittsburgh's Heinz Field.
Pittsburgh, winner of the AFC North title, had a first-round bye in the playoffs.