Smith and head coach Norv Turner being fired at the end of the season was "pure speculation".
According to the San Diego Union-Tribune, club sources have confirmed that both men will go, a report that prompted Chargers president Dean Spanos to issue a statement.
"There is only one person in this organization who will make those decisions and that's me, and I haven't shared my thoughts with anyone," Spanos said.
"I will make my evaluations at the end of the season. Anything coming out now - from sources or otherwise - is pure speculation."
Most Chargers fans would probably like to see some changes made at the top with the team on track to complete a losing season for the first time since 2003, when they went 4-12.
Under Turner's guidance, San Diego have gone 4-8 in this campaign, losing their last four games.
Turner has a 53-39 record since taking over from Marty Schottenheimer in 2007. He led the Chargers to the AFC Championship game in his first season, and the team went on to win the AFC West title in 2008 and 2009.
However, they have not made the playoffs since they went 13-3 in 2009 and have been widely regarded as an underachieving franchise given the relative strength of their roster. (Reporting by Mark Lamport-Stokes in Los Angeles; Editing by Patrick Johnston)
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