Robert Quinn is coming off a breakout 2013 season in which he had 19 sacks. (Getty Images)

Star defensive end Robert Quinn and the St. Louis Rams are close to an agreement on a multi-year extension, a league source told Yahoo Sports.

There is optimism in Quinn's camp that a deal can get done before Week 3, the source said. Quinn is believed to be targeting a deal that would pay him in the $15 million per season range on a four- to six-year extension.

Quinn, a first-round draft pick in 2011, led the Rams with a career-high 19 sacks last season. He also forced seven fumbles in a Pro Bowl season that saw only one man, Indianapolis' Robert Mathis, have more sacks than him.

As a No. 14 overall pick, the University of North Carolina product was one of 11 defensive linemen in the 2011 first-round draft class. Selected ahead of him were Buffalo's Marcell Dareus, Houston's J.J. Watt and Detroit's Nick Fairley.

Watt recently set the market for star defensive linemen after signing a reported $100 million deal that included a $51.87 million signing bonus, a record deal for a defensive player.

The Rams picked up the fifth-year option on Quinn's current deal in August. He's scheduled to make about $3 million this season and about $6.9 million in 2015.