Sources: Giants plan to open contract talks with Leonard Williams before Thanksgiving

Newly acquired defensive lineman Leonard Williams will make his Giants debut Monday night against the Cowboys, and if New York has its way, the former Jetwill be spending his future with the Giants as well.

The Giants would like to re-sign Williams, whose contract expires after this season, and are planning to open contract talks with him before Thanksgiving, sources tell ESPN.

Until then, the idea is for each side to get to know each other and for all to assess how long they want their relationship to last.

The Giants traded for Williams with the idea to re-sign him, even including a clause that turned the fifth-round pick they sent to the Jets into a fourth-rounder if they can consummate an extension with Williams before the league year begins in March.

Giants general manager Dave Gettleman told the team's website this past week that his goal is to sign Williams to a long-term deal.

"We gave up a three and a five," Gettleman said. "Our goal is to sign him long-term. He's only 25 years old. And obviously talented. He's a piece you can build around."

Williams is looking forward to a fresh start in the same state in which he spent the first five seasons of his NFL career. Some sources around the league felt he was putting too much pressure on himself to get more pressure on the quarterback, and a change of scenery should elevate his performance and make the Giants want to re-sign him even more.

Williams, 25, hasn't missed a game in four-plus seasons, but he hasn't produced as a pass-rusher, recording just 17 career sacks, including only two in the past 18 games.

ESPN's Rich Cimini contributed to this report.