Tuesday marked the first day Giancarlo Stanton was eligible to be activated off the 10-day injured list.

But it does not sound as if the veteran DH, dealing with a “low-grade” right calf strain, is actually close to a return.

Stanton has not yet started doing any kind of running, manager Aaron Boone said Tuesday, as the 36-year-old is still feeling the effects of the lingering calf issue.

“He’s doing OK, and he’s hit some,” Boone said before the Yankees beat the Rangers 7-4.

“[It’s lingering] a little bit. It still feels minor, but not ready to push it yet.”

When Stanton landed on the IL — four days after suffering the injury jogging between first and second base in an April 24 game against the Astros, with the club waiting to see if he might be able to avoid a stint — the Yankees were hoping it would be a shorter stay.

But Stanton has had a history of soft-tissue injuries in his legs, so they said they were not going to push anything to have it turn into something more significant.

In the meantime, Jasson Domínguez has mostly filled the DH role — after avoiding a serious elbow injury when he was hit by a pitch last Wednesday — entering Tuesday batting .273 with an .833 OPS in six games.

He went 0-for-4 in Wednesday’s win.

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Ben Rice was out of the lineup for a second straight day Tuesday, still dealing with soreness from a left hand contusion he suffered Sunday.

The slugging first baseman was hoping to pick up a bat at some point Tuesday to see how much improvement he had made, but was mostly relegated to getting treatment.

“Better today,” Rice said before trying to swing.

Paul Goldschmidt started again at first base in Rice’s place and went 2-for-4 with a home run.

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Carlos Rodón made his third and likely final rehab start Tuesday night with Triple-A Scranton/Wilkes-Barre — throwing 85 pitches across 6 ¹/₃ innings in which he gave up six runs (five earned) — as long as everything goes well in the coming days.

The plan is for the left-hander to make his next start with the Yankees, Boone said Tuesday, assuming he comes out of the start healthy as he finishes off his comeback from October surgery to remove loose bodies and shave down a bone spur in his left elbow.

“I’m up to do whatever they want me to do,” Rodón said at Polar Park. “I’ll be ready when they call my name. That would be great.”

Rodón said his stuff could have been crisper, but he got done what he wanted to get done in terms of increasing his workload.

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Gerrit Cole also made a fourth rehab start Tuesday with High-A Hudson Valley — building up to 69 pitches while giving up five runs across 4 ¹/₃ innings — though there was nothing imminent in regards to his return as he goes through a longer comeback from Tommy John surgery.

“I don’t know for sure, but I still think he’s a little bit of ways away,” Boone said.

— Additional reporting by Dan Martin in Worcester, Mass.