The Rams own the 16th overall pick, which is where ESPN draft analyst Mel Kiper Jr. projects as the landing spot for Austin.
The former Dunbar star is also expected to visit the Tampa Bay Buccaneers this month.
Austin participated in the Ravens' local prospect day last week at team headquarters. He met with the Ravens at the NFL scouting combine.
Austin ran the 40-yard dash in 4.34 seconds at the combine.
Although undersized at 5 feet 8, 174 pounds, Austin's moves and acceleration are rare.
"I’ve been a little guy my whole life," Austin said during the combine. "I’m a little guy, but I play big."
Austin had a stellar career for the Mountaineers and a strong performance at the combine. He caught 288 career passes in college for 3,413 yards and 29 touchdowns, also rushing for 1,033 yards and six touchdowns.
Last season, Austin caught 112 passes for 1,289 yards and a dozen touchdowns. He rushed for 643 yards and three touchdowns.
"He's a phenomenal player,” Kiper said during a conference call. “I saw him in high school here at Dunbar in Baltimore, and he was outstanding. He was a man among boys. He's just tremendously electrifying, great quickness. I think Tavon is going to have a heck of a career.
“He is a touchdown maker, he is a scoreboard changer. You can get him the ball in terms of a running game, you can get him the ball on reverses, the wide receiver screens to get him in space, the return game. He’s dynamic.”