Sources said Hafner likely would be offered a one-year, incentive-laden major league deal.
WEEI in Boston first reported the Yankees' interest.
Hafner's career has been derailed by injuries. For four seasons (2004-07), he was one of the best players in baseball, finishing in the top eight in AL MVP voting each of those years.
In each of the past five seasons, however, he has played in more than 100 games only once. In 2012 with the Indians, he hit .228 with 12 homers and 34 RBIs in 66 games. He turns 36 in June.
From the right side, the Yankees could use a rotation of players to DH, much as they did in 2012. Eduardo Nunez, if he makes the team, could be one bat, while the Yankees also could use it as a resting stop for older players such as Derek Jeter, Kevin Youkilis and, if he returns, Alex Rodriguez.