Speaking to reporters Thursday, Woods acknowledged he's happy with his deal but hopes to play with the Rams well beyond 2021.
"You want to get paid for what you're worth," he said. "I want to play here for the rest of my career."
The Rams did restructure his deal last year to give him an extra $1 million in base salary in 2019 and a fully guaranteed $2 million bonus for 2020, per ESPN's Adam Schefter.
That move came after Woods led the Rams with 1,219 yards and tied for the team lead with six touchdown receptions in 2018. He was also instrumental in their run to the Super Bowl that season with at least eight targets and five receptions in all three playoff games.
Woods put together another strong performance last season. The 28-year-old finished with 1,134 yards and set career highs with 139 targets and 90 receptions.
Based on the last two seasons, Woods has outperformed the five-year, $34 million contract he originally signed in March 2017. He is set to make $9 million in base salary in 2021 before he becomes a free agent in 2022.