Suzuki, 39, finished this past season with a .283 batting average and a .307 on-base percentage. He could be slated as the Yankees' every-day right fielder this upcoming season since free agent Nick Swisher is not expected to return.
After being acquired in late July from Seattle, Suzuki reverted to being a very solid player, batting .322 in 67 games with the Yankees. In 95 games with the Mariners, he batted just .261 with a .288 on-base percentage.
Suzuki embraced playing for the Yankees and sounded as if he wanted to return to the team by the end of the year.
Even if Suzuki officially returns to the Yankees, their outfield situation will not be fully set. Sources have said that the Yankees are listening to offers for center fielder Curtis Granderson, and there still is an outside chance that New York could bid for free agent Josh Hamilton.
The Yankees also may move Granderson to left field and shift Brett Gardner into center field. The Yankees are likely to add a right-handed hitting outfielder, as well. They have interest in Scott Hairston, among others.
ESPN's Buster Olney contributed to this report.