The Rams are expected to send draft picks to the Chiefs in exchange for Peters, a source told ESPN's Adam Schefter.
Peters would presumably step in as the Rams' primary cornerback, which might spell the end of Trumaine Johnson's tenure with the team. Peters has compiled 19 interceptions in his first three NFL seasons and was named first-team All-Pro in 2016, the second of back-to-back Pro Bowl appearances.
But Peters also joins the Rams with some character concerns. He was thrown off his college team at Washington for an altercation with an assistant coach. In December, he was suspended by the Chiefs for one game after tossing an official's penalty flag into the crowd and then retreating to the locker room without being ejected during a game against the New York Jets.
Peters was also seen at different times on the sideline last season shouting at defensive coordinator Bob Sutton or others. In at least one instance, he directed expletives at a group of fans behind the Chiefs' bench. The Rams are hopeful that a change of scenery can help fix that.
Rams coach Sean McVay, who was at the Westin Hotel in Kansas City, Missouri, on Saturday to accept his NFC Coach of the Year honor at the 101 Awards, was asked about the trade.
"Right now, just because of where we're at in the league year, you can't make it official, so you have to be careful with some of the tampering," McVay told the Kansas City Star. "But in a quick nugget, he's a great player."
McVay also talked about his team's culture.
"These are grown men, and it starts with the mutual respect that exists, where they know it's about developing and building relationships," McVay told the Star. "If we're going to ask our players to be coachable, we've got to be coachable as coaches as well. That displays an ownership and an accountability that we try to all have and makes the players more receptive to the messages we try to implement."
As for discipline, McVay said his players "know exactly what the expectations are, what our standards are, and they know what it is to do it the right way."
The Peters acquisition gives the Rams salary-cap flexibility, which they could use on pending free agents such as safety Lamarcus Joyner and wide receiver Sammy Watkins. It also helps them sign defensive tackle Aaron Donald to an extension that is expected to eventually make him the game's highest-paid defensive player.
ESPN's Alden Gonzalez and Adam Teicher contributed to this report.