With the Leonard Williams trade to the Giants, Chris Mortensen looks at other Jets who could be moved. (0:47)

The New York Giants made a rare trade with the rival Jets for defensive lineman Leonard Williams, a source told ESPN's Adam Schefter on Monday.

The Jets will receive a third-round pick in 2020 and a fifth-rounder in 2021, a source told Schefter. The fifth-round pick in 2021 will become a fourth-rounder if Williams signs an extension with the Giants before the start of the 2021 league year. The Jets are paying $4 million of the $6 million remaining on Williams' contract this year.

Williams joins a Giants defense that desperately needs an influx of talent. What complicates matters is that Williams, a first-round pick in 2015, becomes an unrestricted free agent at the end of the season.

The Giants (2-6) seem likely to try to re-sign Williams this offseason. If not, they would be eligible to recoup a compensatory pick for the following year.

The Jets concluded that Leonard Williams is not part of their long-term plan. Noah K. Murray/USA TODAY

The addition of Williams continues general manager Dave Gettleman's investment in the Giants' defensive line. Since becoming the GM, he has added Williams, Dexter Lawrence with the 17th overall pick this year and B.J. Hill in the third round the previous year.

Still, the Giants' interior defensive linemen had accounted for just six sacks in the first half of this season. While not a prolific pass-rusher, Williams instantly becomes one of the Giants' best threats on the interior.

Out of playoff contention, the Jets started to address their future, loading up as they head into another rebuilding cycle, this time under first-year general manager Joe Douglas.

The Jets decided to part with Williams, drafted sixth in 2015, after concluding he's not part of their long-term plan. He's only 25, but he's making $14.2 million.

Instead of reinvesting in Williams, whom sources believe will command at least $10 million a year on the open market, Douglas opted for draft capital.

The Jets, reeling under first-year coach Adam Gase, are 1-6, mainly because of an anemic offense. They travel to Miami to face the Dolphins on Sunday.

Gase said he won't comment on the trade until it's official, but he acknowledged that he and Douglas spoke to Williams on Monday morning to give him a "head's up."

"Leonard has done everything we've asked him to do," Gase said. "He's worked hard, he's done a great job in practice. He has fought as hard as anybody every game."

Williams hasn't missed a game in four-plus seasons, but he's considered a disappointment because he hasn't produced as a pass-rusher. He has 17 career sacks, including only two in the past 18 games.

The current and previous coaching staffs defended Williams, saying he was strong against the run and helped others by drawing frequent double-teams. In the end, though, he never became the dynamic player that many expected.

In 2015, the Jets were stunned and happy that Williams slipped to them with the sixth pick. Some evaluators in the league felt he was the best prospect in the draft.

He was the first choice of former GM Mike Maccagnan, who was fired in May. The 2015 draft is wiped out; not one player remains on the Jets roster.

In recent days, Williams took a pragmatic approach to the trade rumors. He said he wanted to remain with the Jets and that he was comfortable in New York, but he also said, "What's cool about it is, it's not this or the streets. Either I'm playing for the Jets or I'm playing somewhere. At the end of the day, I'm still going to be playing. I feel like I have a lot of years left in me in my career."