ESPN reported Monday that since the sides could not reach an agreement on a contract extension, the Cowboys will use the franchise tag on the defensive end, who is coming off a breakout season.
By applying the franchise tag, Lawrence will be paid $17.5 million next season unless the sides reach an agreement on a new contract by the league-imposed July 16 deadline.
Lawrence is represented by David Canter, who also is New York Giants defensive end Olivier Vernon's agent. Vernon inked a five-year, $85 million deal with the Giants two years ago and Lawrence is hoping to get a similar contract.
Lawrence, 25, started every game last season and finished with 14.5 sacks, tying him with Jacksonville's Calais Campbell for second in the league. He recorded 7.5 sacks in Dallas' first three games and had a sack in the first seven games en route to earning a Pro Bowl berth.
Lawrence's breakout season occurred after he underwent back surgery for the second straight offseason in January 2017.
The Cowboys drafted Lawrence with their second-round pick in 2014 out of Boise State. In four seasons with the Cowboys, Lawrence has 23.5 sacks and 133 tackles.