"We know and understand that it's probably not going to happen that we have him this year," Thompson told NBC Sports Washington on Tuesday.
Smith was lost for the 2018 season after sustaining a compound fracture in his right leg during the Redskins' 23-21 loss to the Houston Texans on Nov. 18. He went on to deal with multiple infections in the leg while recovering from surgery.
Sources told NFL Network in January that the Redskins are planning as if they won't have Smith next season. The team also believes he'll miss the 2019 season and would be "pleasantly surprised" if he is ready for the season, according to that report.
Smith, 34, was spotted in January attending a Washington Wizards game. The 14-year NFL veteran was using crutches and wearing a large metal brace on the leg as he watched the Wizards beat the Detroit Pistons in Washington, D.C.
There has been some concern this offseason that Smith's injuries are of the career-ending variety. The three-time Pro Bowl selection completed 62.5 percent of his passes for 2,180 yards, 10 scores and five interceptions in 10 starts for the Redskins before the injury. Smith led the Redskins to a 6-4 start, before the team went 1-5 down the stretch to finish third in the NFC East.
Colt McCoy came off the bench to replace Smith, but also was lost for the season when he broke his leg in December. Smith counts as $20 million toward the Redskins' salary cap in 2019. He has a $21 million cap hit in 2020. McCoy signed a two-year contract with the Redskins in July.