Yankees intend to keep Gardner, will try to move Ichiro instead
The Yankees like Gardner and want him to play left field.
The immediate speculation following the acquisitions of star outfielders Jacoby Ellsbury and Carlos Beltran was that Gardner could be on the block since he'd have to move off center field, but while the Yankees may be receiving calls on him they like the combination of him and Ellsbury covering the Yankee Stadium outfield. Ichiro is the one they wouldn't mind trading.
The issue may be that Ichiro has a limited trade market. The Giants showed interest at the time the Yankees acquired him but, there's no evidence they are interested this time.
The Giants would have had interest in Gardner ... if only he were available.