The teams are in the final stages of agreeing to a deal, ESPN's Adam Schefter reported. It is not immediately known what the Chiefs will receive in return.
The potential trade is the second offseason blockbuster involving the Chiefs, who will send quarterback Alex Smith and a third-round draft pick to the Washington Redskins in exchange for cornerback Kendall Fuller.
Both deals will not become official until the start of the league year on March 14.
The move to acquire Peters could be construed that the Rams are interested in letting cornerback Trumaine Johnson walk in free agency. Johnson had 65 tackles, two interceptions and one forced fumble in 16 games this past season.
Peters, who was the 18th overall pick in the 2015 NFL Draft, was named the NFL Defensive Rookie of the Year and is a two-time Pro Bowl selection. He recorded 19 interceptions in three seasons, including five in 2017 to go along with 46 tackles and four forced fumbles in 14 games.
The 25-year-old Peters, however, was suspended for one game this past season following his actions in a 38-31 loss to the New York Jets on Dec. 3.
Peters received an unsportsmanlike conduct penalty following a defensive holding call against teammate Steven Nelson during an unsuccessful two-point conversion try by the Jets. Peters picked up the official's flag and threw it into the stands, then walked off the field to the locker room without being ejected.