Nakajima was recently in Arizona and toured the D-backs' facilities.
Shortstop has been an area of need for the D-backs this offseason, though they did acquire Cliff Pennington from the A's in October.
Nakajima was posted by the Seibu Lions last year and the Yankees won his negotiating rights with a $2 million posting fee. However, the two sides were unable to reach an agreement, so he returned to Japan where he had a slash line of .311/.382/.451 to go along with 13 homers and 74 RBIs.
The D-backs have also been linked this offseason to Japanese closer Kyuji Fujikawa.
The right-hander met recently with the D-backs, but the club does not appear to be as interested after having acquired Heath Bell from the Marlins.
D-backs general manager Kevin Towers said Tuesday morning that he was more interested in acquiring a lefty for the bullpen, which he did later in the day by picking up reliever Matt Reynolds from the Rockies.