Cousins, who will earn $23.9 million this season, and the Redskins can't negotiate a long-term deal until the season ends by virtue of being unable to come to an agreement by Monday's deadline.
The 28-year-old is open to working a deal with the Redskins after this season, a source familiar with the situation told ESPN's Adam Schefter.
Washington offered Cousins a five-year deal worth approximately $20 million per season earlier in the offseason with "low guarantees," ESPN reported, citing a source.
The Redskins can use the tag on him again next offseason for a third straight year, but it would cost the team $34.7 million to franchise him again for 2018. Cousins would be unable to negotiate with any other teams.
Cousins threw for 4,917 yards with 25 touchdowns and 12 interceptions in 2016 and also posted a 97.2 passer rating last season. Cousins' 12,113 yards in five seasons with Washington ranks sixth on the franchise's all-time passing yards list. He is 239 yards behind Billy Kilmer for fifth.