ESPN first reported the Yankees' interest early Monday and later reported the Dodgers are also in pursuit of the 29-year-old, who fanned 103 batters and walked only 17 in 62 1/3 innings in 2014.
Miller's agent, Mark Rodgers, told the New York Post there is no frontrunner and several teams are interested in his client.
"I am talking to several teams about Andrew, and it has been fairly widely reported that the Yankees are one of the teams interested," Rodgers told the newspaper. "They are still interested, but I will not elaborate on the talks. There is a natural progression ongoing, and we are sorting through the issues."
Other clubs reportedly showing interest include the Tigers and Red Sox.
The Yankees also are still in pursuit of free-agent closer David Robertson, and could sign Miller, Robertson or both to team with Dellin Betances in the back end of the bullpen.
As for Los Angeles, adding Miller would help bridge the gap to closer Kenley Jansen and stabilize a 'pen that last season ranked near the bottom of the National League in ERA with a 3.80 mark.
Cash Kruth is a reporter for MLB.com. Follow him on Twitter at @cashkruth. This story was not subject to the approval of Major League Baseball or its clubs.