Head coach Jay Gruden "very strongly" believes the Pro Bowler won't be traded.
Williams dealt with knee injuries throughout last season as well as a medical scare with a "growth or tumor on his head" in April, but he is now fully healthy, per Rapoport.
Williams is frustrated with how the medical staff handled the medical scare as well as his knee and thumb injuries over the past two seasons, according to Les Carpenter of the Washington Post.
Jason La Canfora of CBS Sports reported last month the 31-year-old doesn't trust the medical team or general manager Bruce Allen and his relationship with the team is "fractured."
Though he has been fined by the team during the holdout, he's expected to remain out into the regular season.
"He's not coming back. Period," a source told JP Finlay of NBC Sports.
After earning Pro Bowl selections in each of the past seven years, Williams would likely be in demand on the open market, but it appears the Redskins don't intend to trade him. He still has two more years remaining on his current contract before he could hit free agency.
Donald Penn and Geron Christian are the Redskins' options at left tackle with Williams unavailable.