Gordon will also demand a trade from the team if he does not get a new deal, Schefter added.
The 26-year-old is heading into the last season of his contract on a fifth-year option worth $5.6 million.
Gordon reportedly received an extension offer from the Chargers that did not align with the contracts of other top running backs such as Le'Veon Bell and Todd Gurley. His dissatisfaction with negotiations led him and his agent, Damarius Bilbo, to address the matter publicly in an effort to either secure a better offer or force a trade.
Bilbo said there's a "strong possibility" the running back could sit out into the regular season if a satisfying outcome is not reached, according to NFL Network's Tom Pelissero.
"He's very serious. He's worked his butt off and the fifth-year option is a result of where he was drafted. It's what it is," Bilbo told NFL Network's Ian Rapoport. "But if we'd gotten a respectable offer, we wouldn't be here. But he felt disrespected. He's very serious."
The two-time Pro Bowler has led the Chargers in rushing yards every year since being selected in the first round of the 2015 NFL Draft. He had 885 rushing yards in 12 games last season and added another 490 yards and four touchdowns through the air.
Chargers training camp is slated to begin July 24.