St. Louis invited Alexander to the team facility on August 2 to take a physical, which he said he passed.
"It went great," Alexander said, by phone, afterward. "Everybody is really excited about me coming in. We're not able to do a deal right now but it's possible something could happen in the next few weeks."
The 6-foot-5, 220-pound Alexander, who turned 22 two weeks ago, also made a trip to Seattle to take a physical for the Seahawks, but was not offered a contract.
Alexander was one of the top playmakers in the country a year ago when he recorded 113 receptions for 1,781 yards and 14 touchdowns. He had surgery in February to repair cartilage damage in his knee and was not drafted. He held hold a pro-day style workout at the end of July and reportedly recorded a time of 4.46 seconds in the 40-yard dash.
"I got a quick chance to meet Danario," Rams coach Steve Spagnuolo said after the wide receiver's visit. "He's a wonderful guy. But other than that, I haven't had a chance to talk to Billy (Devaney, the team's general manager)."
The Rams coach and general manager were expected to discuss whether they want to sign the dynamic wide receiver to add to a receiving corps that figures to be one of the biggest position battles of training camp.
"I've always said we're always looking all the time to upgrade at any position," Spagnuolo said. "If we think there's a guy out there that can create competition to a group that is already existing, then we bring him in. We bring guys through here you work them out — Billy's staff does that — then you make a decision after that."
Devaney said after Alexander took the physical that the Rams needed the wide receiver to be in football-ready shape so that if the team signed him to a rookie free agent contract, he would be ready to practice right away rather than stay on the sidelines while working his way into shape.
The Rams currently have 10 wide receivers on their training camp roster.
Spagnuolo was asked on Thursday if any particular wide receiver had separated himself from the rest and he said, "Not really. I think they're all right there, competing against each other."