The San Francisco 49ers are also among the teams showing interest in Norman, the source said. However, Jacksonville Jaguars GM Dave Caldwell said Friday that they're likely aren't going to be a contender for Norman's services.
Norman's deal, when complete, is expected to be worth between $14 million and $15 million per year, sources told Schefter. Five-year deals are being discussed with both Washington and San Francisco.
The Jaguars' Caldwell said that type of price tag is causing a "pretty significant" gap -- especially for a player that "I don't know if it would make us significantly better."
"I think there's a lot of dynamics that go into it," said Caldwell, who has been in contact with Norman's reps but has not make an official offer. "I think he's a good player. I think we just have to kind of stick to what we value."
Friday's visit with Washington is Norman's first since the Panthers' decision.
Carolina general manager Dave Gettleman said Thursday that the team chose to rescind Norman's tag because of the flexibility the team would have without Norman counting toward its salary cap number and because it was unlikely to reach a long-term deal with him.
Norman was seeking between $15 million and $16 million a year, according to a league source.
The Redskins need a cornerback but would have to free up more cap room to sign Norman. According to ESPN Stats & Information, they have only $11.4 million available.
The 49ers have $53 million in cap space this year and $55 million in 2017, meaning they could offer Norman a deal longer than one year and worth an amount comparable to what other top cornerbacks make.
On Thursday, Gettleman gave no indication whether he thought Norman might return to Carolina. The Panthers regained $13.952 million in cap space after rescinding the tag on Norman.
"The more we thought about it, the more flexibility that $14 million would give us ... we just kept talking and talking," Gettleman said. "I have a great belief that in order to get the right answer, you have to ask the right questions.
"We kept asking ourselves that question, and this is why we made the decision we made."
ESPN's Mike DiRocco contributed to this report.