On Friday, Jane Slater of the NFL Network noted a source said the cornerback "should be good to go" barring a setback involving his rib injury over the next two days.
Ian Rapoport of NFL.com reported Norman also suffered "small damage to his lung lining" in addition to the rib fracture.
Norman originally suffered the injuries during the Redskins' 29-20 loss to the Kansas City Chiefs in Week 4. They had a bye in Week 5 and he's missed each of the last two games, a victory over the San Francisco 49ers and a loss against the Philadelphia Eagles, while recovering.
The 29-year-old Coastal Carolina alum provided an update following Thursday's practice.
"I said last week, 'Today was a good day.' It was. But I didn't play last week. So maybe I want to change a little bit this week," he told reporters. "But no, again, today was a good day. It feels a little sore, but that comes with the territory of that injury. But it felt fine. I don't see any problems or reason why I can't [play]."
Norman's return would be a welcome sight for a Washington defense that ranks 24th in yards per passing attempt and will be tasked with containing Dez Bryant on Sunday.
Quinton Dunbar and Kendall Fuller would once again be thrust into more high-profile roles if the veteran corner is unavailable against the NL East rival Cowboys.