Cashman says "there's no guarantees in this stuff" that Rodriguez will be able to play this year.
The 37-year-old Rodriguez had surgery on his left hip last week. The team said the rehabilitation time was expected to be six months, which would sideline the star slugger until the All-Star break.
On Friday, Cashman said it was possible A-Rod could be out all year.
"Yeah," Cashman told WFAN radio. "I think because (of) the serious nature of the surgery and the condition that he's trying to recover from, you know, there is that chance."
"I can't say it's not possible that he won't be back," he said.
The Yankees signed free agent Kevin Youkilis during the offseason to play third base while Rodriguez is out.
Cashman said Rodriguez is doing everything "in his power to put himself in the position to get back and be healthy and productive."
"Best case scenario, yeah he should be back," Cashman said. "Worst case scenario, he won't be back, or there might be something in between."
A 14-time All-Star, Rodriguez hit .272 with 18 home runs and 57 RBIs in 122 games last year. The three-time AL MVP was benched in three of nine postseason games and pinch hit for in three others, batting just .120 (3 for 25) with no RBIs in the playoffs.
Rodriguez had surgery on Jan. 16 to repair a torn labrum and reshape a bone to alleviate an impingement. He has 647 career homers and is due $114 million over the next five years as part of his record $275 million, 10-year contract.
NOTES: RHP David Robertson and the Yankees reached a one-year deal, avoiding arbitration. The reliever had asked for $3.55 million and the team offered $2.85 million.