TORONTO — The clock is ticking on DJ LeMahieu and whether he’ll be able to be a part of the Yankees’ postseason plans.

Aaron Boone said Monday that LeMahieu would increase his pregame workload on Tuesday in his attempt to show he can still perform at a high level despite the right toe inflammation that has plagued him for much of the second half.

“He’s gonna do a little more these next couple days,’’ Boone said. “He’ll hit early [Tuesday] and test it more intensely.”

Asked if there was enough time left in the season to get LeMahieu back, Boone said, “We’ll see. It’s in the hands of the medical team and DJ, when that day is we can work him back in. I feel he’s gonna come back in some way, shape or form then we’ll see what we’ve got.”

LeMahieu hasn’t played since Sept. 4, and even before that was significantly impacted by the toe injury.

LeMahieu was hitless in his last four games, going 0-for-15 — and was 2-for-38 in his last 10.

Since Aug. 9, LeMahieu is 10-for-78 with no extra-base hits in 85 plate appearances. He struck out 17 times in that 20-game stretch with an OPS of just .307.

The Yankees continue to believe there’s a chance Matt Carpenter (fractured left foot) will return, with general manager Brian Cashman telling The Post’s Joel Sherman that Carpenter could even be on the roster for the final series of the regular season in Texas.

“I think we’re holding out hope, but we’re a ways away from knowing if that’s possible,’’ Boone said. “A lot depends on how this week unfolds.”

But Boone added Carpenter is doing more weight-bearing activities on the foot and the Yankees are keeping him in mind as they shape their roster for the final days of the season.

Frankie Montas is expected to start throwing again this week, according to Boone.

“We’re hopeful it’s this week,’’ Boone said of the right-hander, who received a second cortisone shot on his troublesome right shoulder. “He’s trending in the right direction.”

Still, Boone made it clear Sunday that Montas, with a 6.35 ERA since arriving in a trade from the A’s at the deadline, is in line to be more of an opener given his lack of workload before the postseason, even if he is able to return.

The Yankees had much bigger plans for Montas when they picked him up from Oakland, but now their playoff rotation is shaping up to be Gerrit Cole, Nestor Cortes, Luis Severino — Monday’s starter — and potentially either Jameson Taillon or Domingo German.

Aaron Judge was back in the leadoff spot on Monday, his 15th straight start at the top of the lineup.

“When we put him there more permanently, we were at a point of the season we were really thin [due to injuries],’’ Boone said. “As we continue to get whole here, it’s continued to make sense.”

Entering Monday, Judge had a 1.293 OPS in 25 games as a leadoff hitter compared to 1.087 in 112 starts batting second.