Multiple teams already have had preliminary discussions with St. Louis about the possibility of trading for the Rams' second overall pick, according to league sources.
The Rams are willing to deal the pick for the right package, according to one source, and the chances are that St. Louis will wind up trading down.
The target at the No. 2 spot is likely Heisman Trophy-winning Baylor quarterback Robert Griffin III.
Griffin will not throw at this weekend's scouting combine in Indianapolis, but he measured in Friday at 6-foot-2 3/8, taller than NFL teams expected.
Griffin also weighed 223 pounds, giving him ideal measurables for the April draft and the NFL.
A handful of teams are expected to be in the market to draft a quarterback -- the Cleveland Browns, Washington Redskins, Miami Dolphins and Seattle Seahawks -- and any trade talks with the Rams are likely to accelerate once the free-agent quarterback market plays out and teams still have a need at the position.
Meanwhile, the order of four other first-round picks were determined Friday via two coin tosses.
The Dolphins will draft eighth. The Carolina Panthers lost and will draft ninth.
In the second coin toss, the Kansas City Chiefs won and will draft 11th. Seattle lost and will draft 12th.
Adam Schefter is ESPN's NFL Insider. Information from ESPN.com senior writer John Clayton was used in this report.