Kings general manager Dean Lombardi told the newspaper he expected the Rangers to speak with Stevens. Stevens remains under contract with the team, but Lombardi previously had said he was going to allow Stevens to pursue other opportunities.
Stevens previously interviewed with the Vancouver Canucks about their vacant coaching job.
Stevens has spent the past three seasons as an assistant with the Kings, first under Terry Murray and for the last year-and-a-half under Darryl Sutter.
Stevens previously coached the Philadelphia Flyers for parts of four seasons, going 120-109-34 and reaching the Eastern Conference Final in 2008.
Former Rangers captain Mark Messier, with the team as a special assistant to the president, told reporters Friday he has interviewed for the job. The Rangers also reportedly have interviewed former Canucks coach Alain Vigneault and former Buffalo Sabres coach Lindy Ruff.