Andrew Marchand of ESPN.com reported the news Monday, noting general manager Brian Cashman "has always been a big fan of Beltran's on and off the field."
Beltran announced his retirement earlier Monday in a post on the Players' Tribune.
Beltran said he "would love to have the opportunity to manage," per Mark Feinsand of MLB.com, and he even pointed to the possibility of taking over the Yankees job.
"I appreciated the way I was treated; my family, the relationship with Brian," he said. "I don't know what they're looking for. Experience as a manager, I don't have that. But I have the passion for the game, I have the knowledge of being able to play the game for a long time. I get along well with the players, with my teammates; I've always taken that to heart, trying to impact my teammates in a positive way.
"I would not discount anything; you're talking about the New York Yankees. You're not just talking about any team in baseball. Not taking anything away from any other organization, but the Yankees are a team that anyone would love to put on that uniform and manage that ballclub."
The job is open because the Yankees parted ways with Joe Girardi even though they reached Game 7 of the American League Championship Series against Beltran's Houston Astros.
Cashman pointed to communications problems within the clubhouse as the main reason behind the decision, per Marchand. New York finished with a winning record in each of Girardi's 10 seasons and won the 2009 World Series in his second at the helm.
Beltran played 20 seasons for the Astros, Yankees, Kansas City Royals, New York Mets, San Francisco Giants, St. Louis Cardinals and Texas Rangers. He was a nine-time All-Star, three-time Gold Glover and two-time Silver Slugger and was named the 1999 American League Rookie of the Year.
He helped the Astros to their first World Series title this season.