If Monday's 4 p.m. ET deadline passes with no long-term contract, Cousins is open to doing a deal with the Redskins after this season, a source familiar with the situation told ESPN's Adam Schefter.
The Redskins could make a last-minute push to get a deal done with Cousins, who was franchised for the second consecutive year.
Cousins, who turns 29 on Aug. 19, wants to play this season under his franchise tag, worth $23.94 million.
According to ESPN, there has been a positive and constructive tone to recent contract talks, but Cousins prefers to wait to do a deal at this time, just as the Redskins preferred to wait to do a deal at this time last year.
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.
Washington also could transition him for $28.7 million, but another team would have the ability to sign him to an offer sheet. The Redskins then would have seven days to match.
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.
No deals reportedly are close for Pittsburgh Steelers running back Le'Veon Bell and Los Angeles Rams cornerback Trumaine Johnson, the other two franchised players who have yet to agree to long-term contracts.
Johnson ($16.74 million) signed his one-year tender, but Bell has not. If no long-term contract is reached by Monday's deadline, Bell will have no choice but to sign his $12.12 million tender.