Almonte was batting .261 with one home run and nine RBIs over 26 games with the Yankees. Hafner hit .205 with 12 homers and 37 RBIs, and Youkilis was at a .219 clip with two home runs and eight RBIs.
"Youk is probably the least probable of the three," manager Joe Girardi said, "and I think Almonte is probably the furthest ahead."
Girardi also said David Phelps, who is working his way back from an elbow strain, will throw a bullpen sometime this week and could be an option in the Yankees' bullpen before the end of the season.
Michael Pineda, who recently began throwing again after being shut down for a month with discomfort in his shoulder, is still just throwing bullpen sessions and likely won't be an option for the Yankees this year.
Bryan Hoch is a reporter for MLB.com. Follow him on Twitter @bryanhoch and read his MLBlog, Bombers Beat. Josh Vitale is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.