Eckstein, 33, signed a one-year, $4.5 million deal with the Blue Jays prior to this season.
A shortstop throughout most of his eight-year career, Eckstein has appeared in six games at second base this season, as well as 14 in 2001. The D-backs are without the services of starting second baseman Orlando Hudson, who suffered a season-ending wrist injury earlier this month.
Eckstein is batting .274 with a .353 on-base percentage in 74 games this year. He has plenty of postseason experience in his career, including two World Series rings with the Angels in 2002 and the Cardinals in '06.
FOXSports.com reported that the Angels are also pursuing Eckstein.
Steve Gilbert is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.