The Yankees' interest in Randolph would be to fill the position previously held by Kelleher, working with the club's infielders and coaching first base during games.
New York interviewed several candidates for their open coaching slots in late October and November but were unable to find a match. General manager Brian Cashman said the team decided to shelve that pursuit of coaches until the new year, opting to focus instead on the free-agent and trade markets.
Randolph, 60, played 13 of his 18 seasons with the Yankees and won six World Series rings in pinstripes, including four as a coach. He managed the Mets from 2005-08 and last held an on-field position as a third-base coach with the Orioles in 2011.
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. This story was not subject to the approval of Major League Baseball or its clubs.