"He's a huge part of what we're doing," McVay said about Woods, who has considerably outplayed the five-year, $34 million deal he signed with the Rams in 2017.
"It's been in the talks," Woods said after practice. "Just praying that it gets done on time and really just trying to go out there and execute what I do on the field and let my play do the talking for me, which it has."
When asked to clarify if there was a deadline to reach a deal, Woods said, "Just urgent, as soon as possible," but he later stated his desire to minimize any future injury concern and sign a contract before a Week 2 matchup against the Philadelphia Eagles.
Before the season opener, Ramsey signed the most lucrative defensive back contract in NFL history: a five-year, $105 million deal that included $71.2 million guaranteed at signing. Two days later, Kupp signed a three-year, $48 million extension.
"Great to be able to get Cooper under contract, so happy for him," McVay said. "And you can expect to see something similar down the line here very shortly, we're working toward for Robert."
Woods said that after Kupp's deal, McVay communicated with him directly, emphasizing that he remained in the team's long-term plans.
"[McVay] just kind of put his arm around me and said he's happy to have me here, been a true competitor since I stepped on his team," Woods said. "He kind of just reassured me that this deal would be taken care of this week."
Woods is scheduled to earn $5 million this season, with his contract set to expire at the end of the 2021 season.
A second-round pick in 2013 by the Bills, Woods played four seasons in Buffalo, producing modest numbers, including 2,451 receiving yards and 12 touchdowns.
He has excelled since returning three years ago to Los Angeles, where he grew up and starred at USC. Woods produced back-to-back 1,000-yard receiving seasons in 2018 and 2019, and last season led all NFL receivers with 577 yards after the catch. On Sunday, in a Week 1 20-17 win over the Dallas Cowboys, Woods had six receptions for 105 yards.
On Thursday, Woods, who turned 28 last April, listed his many roles in McVay's high-powered offense. He said he had proved his worth since his rookie stint in Buffalo.
"Now you find yourself in an elite situation, where you're finally able to do what you're capable of," Woods said. "So now it's time to get paid what I'm capable of being paid -- up there with the best of the best."
Over the past three seasons, Woods ranks among the top 11 NFL receivers in receptions, receiving yards and yards after catch.
Along with Kupp, McVay called Woods a pillar of the offense.
Since joining the Rams, Woods has caught 238 passes for 3,239 yards and 13 touchdowns. He's also rushed for 298 yards and two scores.