DETROIT — Dellin Betances is getting closer to making his season debut with the Yankees, but the right-hander will continue his rehab assignment with Double-A Trenton for now.

Manager Aaron Boone said Betances still has some work to do before he finally joins the Yankees after missing the entire season, first with a shoulder impingement followed by a lat strain.

“He felt a little better than last time, but we want to see him continue to build up,’’ Boone said before the Yankees-Tigers game was rained out Wednesday at Comerica Park. “He’s not all the way back to where he would want to be or where we would want him to be. … If we can continue to build him up while we have the opportunity down there, we’ll do that.’’

But Boone also called Betances’ scoreless inning with Trenton “another step forward.”

Betances could pitch in Trenton’s playoff series either Thursday or Friday and he’d figure to get to The Bronx at some point during their upcoming homestand, which starts Tuesday.

“We felt like the overall command of his fastball was better,’’ Boone said of Betances’ second rehab outing. “He spun some really good breaking balls. He struck out a couple guys. We’ll continue to build him up. What we’ve seen historically from Dellin is he continues to get better as he builds up outings and that’s what we expect.”

Jordan Montgomery, who threw three innings for Trenton on Tuesday in his comeback from Tommy John surgery, may join the Yankees in the coming days, as well, though the team is looking at the lefty more for next season than the stretch run.

Another lefty, Stephen Tarpley, is expected to rejoin the Yankees on Thursday.