Yankees manager Joe Girardi said a decision will come Monday.
''It's something I have to talk to him about,'' Girardi said Saturday. ''See where he's at physically.''
Rodriguez, who turns 40 in July, was suspended for the entire 2014 season because for violations of baseball's drug agreement and labor contract.
If A-Rod doesn't play in Tuesday's road game in Clearwater, his debut could come in Wednesday's spring home opener with the Phillies.
''We'll see where he's at,'' Girardi said.
With the re-signing of Chase Headley to start at third base, Rodriguez is competing for at-bats as the designated hitter. He might get limited playing time at third and first base.
Rodriguez ranks fifth on the career home run list with 654. He has not played a full season since 2007 because the suspension, operations on both hips and other injuries.
Girardi said it's possible Rodriguez will make more exhibition road trips than normal for a veteran player in order to get additional at-bats.
''I'll try to pick my spots,'' Girardi said. ''It's communication on how he feels.''
Girardi plans to announce his starting pitchers for the first few spring training games on Sunday. The list will not include Masahiro Tanaka or CC Sabathia.
Tanaka, who missed 2 1/2 months last season with a partially torn ulnar collateral ligament in his right elbow, will throw batting practice for the first time in the next couple days.
Sabathia, hobbled by a degenerative cartilage problem in his right knee last season that resulted in season-ending surgery in July, has one more bullpen session before advancing to batting practice.
NOTES: Dallas Cowboys coach Jason Garrett and his wife spent around three hours at Steinbrenner Field. Jason Garrett talked with the players, and then watched the workout moved indoors because of rain with his wife. ... Yankees GM Brian Cashman has told SS Didi Gregorius to be himself and not try to match the play of retired captain Derek Jeter. ''I just want him to be the best player he can be,'' Cashman said. ... Girardi said 2B Stephen Drew will get some playing time at shortstop this spring.