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"We have a tentative date, but I'm not going to reveal it," Cashman said Friday.
Asked if Rodriguez still is on the original schedule for the procedure, Cashman said: "That's correct."
The Yankees announced Dec. 3 that Rodriguez would have surgery in January after four to six weeks of "pre-rehabilitation." Rodriguez, who had surgery on his right hip in 2009, will have his left hip operated on this time. He is not expected back until June at the earliest.
The Yankees signed Kevin Youkilis to play third base until A-Rod returns.
With pitchers and catchers reporting to spring training Feb. 12 -- earlier than usual because of the World Baseball Classic -- Cashman still is looking to add a righthanded-hitting outfielder.
"I feel we're an unfinished product," he said. "We have a lot of strengths, but we have some areas of exposure that we need to shore up between now and Opening Day."
With an all-lefthanded-hitting starting outfield, the Yankees have interest in former Met Scott Hairston, but he is said to be looking for a two-year deal. Cashman, citing major-league rules, declined to speak about specific free agents.
Cashman signed former Braves outfielder Matt Diaz to a minor-league deal last month. Diaz, 34, hit .222 with two homers and 13 RBIs in 51 games for the Braves in 2012, but against lefties, he has a career .324 average with 31 home runs in 945 at-bats, compared with .258 and 14 in 918 at-bats against righties.
The Yankees claimed first baseman / outfielder Russ Canzler off waivers from the Indians on Friday. Canzler, 26, is a righthanded hitter who appeared in 26 games for Cleveland in 2012. He hit .269 with three home runs and 11 RBIs.
To make room for Canzler on the 40-man roster, the Yankees designated outfielder Chris Dickerson for assignment.
On other matters:
Cashman said he is not looking to add a catcher before spring training, meaning the Yankees will choose from among Francisco Cervelli, Chris Stewart, prospect Austin Romine and recent signee Bobby Wilson to replace Russell Martin.
"Our catchers are here on the roster," Cashman said. "It was either Russell Martin or we're going from within."
Closer Rafael Soriano still is a free agent, but a return to the Yankees seems unlikely. Soriano opted out of the final year of his Yankees deal after saving 42 games in place of the injured Mariano Rivera.
"I cannot talk about players on the free-agent market," Cashman said. "But I am not looking for bullpen help, I can tell you that."
Cashman said he does not know which Yankees will participate in the World Baseball Classic.