On Friday, Calvin Watkins of The Athletic reported the sides are expected to talk about a new deal before the deadline, but Lawrence is willing to play under the one-year, $17.1 million tag if a long-term agreement can't be reached.
The 26-year-old Boise State product is coming off a breakout year for the Cowboys.
He racked up 58 combined tackles, 14.5 sacks, four forced fumbles and two fumble recoveries while playing all 16 regular-season games. His sack total was tied for the second-highest in the NFL behind only the Arizona Cardinals' Chandler Jones (17).
Lawrence, a second-round pick in 2014, had nine sacks across his first three seasons.
After signing the franchise tag in early March, the South Carolina native told NFL Network's Jane Slater he was prepared to show the 2017 campaign was no fluke.
"I feel like they have given me the opportunity to really break the bank next year," Lawrence said.
He's not the only marquee pass-rushing superstar seeking a new deal. The Oakland Raiders' Khalil Mack, Los Angeles Rams' Aaron Donald and Houston Texans' Jadeveon Clowney are in the same boat.
So waiting an extra year to ink the extension to see what those fellow edge-rushers receive could earn him more money, assuming he posts another top-tier statistical campaign in 2018.