On Friday afternoon, the Rams fully expected to be negotiating right up until draft time, set for 6 p.m. ET, a source told ESPN's Rachel Nichols.
The Rams had the No. 1 pick Thursday and used it to select quarterback Sam Bradford of Oklahoma.
Clausen was still recovering earlier this month when he worked out for NFL teams, three months after surgery to repair torn tendons in his right foot.
Clausen said he wanted to be able to show he could drive the ball, adding his toe felt fine but the top of his ankle was weak after being in a boot for eight weeks.
McCoy's shoulder injury from January's national title game was declared 100 percent healed in early March, several weeks before he worked out for NFL teams. He did not need surgery, just time to rest and rehab.
Information from ESPN NFL Insider Adam Schefter and The Associated Press was used in this report.