The four are: Jose Ascanio, a right-handed reliever; Jeff Baisley, a corner infielder; Wil Ledezma, a left-handed reliever; and Shane Lindsay, a right-handed reliever.
A tentative agreement has been reached with Alberto Castillo, a 35-year-old left-hander from Cuba who had a 2.31 ERA in 17 games in 2011 for the D-backs, his eighth organization. He missed August with shoulder tendinitis.
Castillo and Ledezma are insurance for Hong-Chih Kuo, who is almost certain to be non-tendered after a trouble-plagued 2011 that ended with a fifth elbow operation.
Ascanio, 26, spent most of 2011 at Triple-A, with an eight-game callup by Pittsburgh, where he posted a 7.11 ERA.
Baisley, 29 later this month, last played in the Major Leagues with Oakland in 2008 and slugged 20 homers with 100 RBIs for the Angels' Triple-A Salt Lake club this year.
Ledezma, 30, is the most accomplished of the group and would seem to have a chance of making the 40-man roster as a situational lefty, especially if Kuo does not return. Ledezma also spent most of 2011 in the Minor Leagues, with 11 games for Toronto.
Lindsay, who turns 27 next month, is an Australian who pitched four games with the White Sox in 2011, but spent most of the year at Triple-A.
Baisley, Ledezma and Lindsay have out clauses to sign with Asian teams.
Ken Gurnick is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.