Kupp tore his ACL in a victory over the Seattle Seahawks in Week 10 last season.
"It's been a long process for sure," Kupp said about his knee rehab. "I've been doing what I can to get back."
Coach Sean McVay said the goal was for Kupp to return in Week 1 against the Carolina Panthers.
"He's like a kid standing on the sidelines that just wants to grab a ball and go play," McVay said. "He's one of those guys that's right on track with where we want him to be."
Kupp, speaking to reporters for the first time since his injury, would not commit to a date when asked when he would like to return.
"I can't predict how I'm going to feel even a week from now," the 25-year-old said. "But the way that things are going, I'm happy with the way that things are trending. Each week there's progress."
Last season, Kupp played a crucial role in the Rams' offense, which produced an average of 421.1 yards and 32.9 points per game. As a second-year pro, Kupp caught 40 passes for 566 yards and six touchdowns.
But the productivity of the offense, and of quarterback Jared Goff, diminished during Kupp's absence.
According to ESPN Stats & Information research, Kupp was part of a five-man skill position group that played a league-high 277 snaps together through 10 weeks, prior to Kupp's injury. When Kupp was not on the field, the Rams' first-down percentage dropped from 47 to 38 percent, and without Kupp, Goff's completion percentage fell from 71 to 61 percent, while his yards per attempt dipped from 9.3 to 7.2.
Goff said Monday that Kupp looked good in his rehab and that he has taken an aggressive approach.
"He's a guy that you gotta always kinda keep pulling back and telling him, 'No, no that's enough. Stop running, stop cutting, you're good,'" Goff said, with a chuckle. "I told him today that he needs like a shock collar because he'll just start running."
McVay said that he would find ways to "get creative" and get Kupp more involved as the offseason program moved forward.
"We're pushing as hard as we can without putting the knee and myself in a bad position," Kupp said.