Jake Odorizzi admitted he’d thought about it.

True, the 29-year-old righty wasn’t drafted by the Minnesota Twins. He was a first-round pick by the Milwaukee Brewers in 2008.

He didn’t debut with the Twins, but rather the Kansas City Royals — whom he’ll face if he makes his final scheduled start of the season.

He hasn’t even thrown the most innings of his career in a Twins uniform. He’s thrown more than twice as many as a member of the Tampa Bay Rays (698) than he has as a Twin (317 after Wednesday night’s game).

But Odorizzi told the assembled media after his start in a 3-1 loss to the Chicago White Sox that he’d be lying if he hadn’t thought it was possibly his final start at Target Field in a Twins uniform. The Twins wrap their home schedule this weekend with the Royals, and Odorizzi is slated to most likely start Game 2 in the American League Division Series — which as of now would be on the road in either Houston or the Bronx.

And since the ALDS is a five-game series, the most likely scenario for Odorizzi’s earliest second playoff appearance would be in a deciding Game 5 — again on the road.

So what might seem like a bit of a stretch on the surface might actually be a cold hard truth. With free agency looming this offseason, it’s possible that Odorizzi has pitched his final game in a Twins uniform at Target Field.

“Yeah I thought about it,” Odorizzi said. “I know how the schedule is going to fall for me. I make one more start on the road and whatever happens there. Playoff schedule — if we make it there — can be a toss up. There was opportunity that was left on the table (Wednesday) to really kind of cap off a really productive season. Hopefully I get that opportunity again. If not, it is what it is.”

For Odorizzi’s part, he pitched well on a night where the Twins offense was unable to get anything going against a cadre of White Sox pitchers. Ivan Nova started and threw the first inning — he’s slated to make a regular start this weekend — and in all, manager Ricky Renteria deployed eight pitchers in the win.

None of the pitchers recorded more than seven outs.

Odorizzi pitched into the sixth, but was lifted after Yoan Moncada doubled home Chicago’s second run of the night, followed by a walk to Eloy Jimenez.

Cody Stashak came in and struck out Zack Collins on three pitches to escape any further damage, giving Odorizzi a final line of 5.2 innings with two earned runs, seven hits, nine strikeouts and a walk. Odorizzi came up just one strikeout short of his third 10-strikeout game this season — both of which have come against Cleveland.

Both of the runs Odorizzi gave up were somewhat serendipitous.

Moncada opened the second inning with a double to left, but it was a play that a more experienced left field would have had little trouble making. Instead, infielder-turned-outfielder Luis Arraez got his glove on it but couldn’t finish the play, and Jimenez drove him home with a single three pitches later for a 1-0 lead.

Odorizzi went on to get 12 outs from the next 13 hitters he faced — including a double play off the bat of Collins — before the White Sox struck in the sixth for their final run against the starter.

Leury Garcia opened the inning with a single, and Tim Anderson replaced him at first after a fielder’s choice. Moncada’s double — his second of the night — stayed in the yard, allowing Anderson to scoot home where a ground-rule double would have placed runners at second and third.

Nevertheless, Odorizzi walked Jimenez and that was it. He threw 94 pitches and 61 were strikes.

“I thought Jake looked really sharp,” manager Rocco Baldelli said. “I thought Jake threw the ball great. He missed a ton of bats. He went out there and dominated. I believe that. We didn’t win the game. It doesn’t sound like maybe the right word to use when you lose the game, but he was great. He threw the ball phenomenally.

“(If) he keeps throwing the ball like that — and he has lately — we’re good to go.”

“I thought I threw the ball pretty darn well,” Odorizzi said. “Some nights that’s enough to get it done; tonight wasn’t one of those nights.”

And regardless of if it was the collateral damage from the late night on Tuesday or just a cumulative effect of playing nine mostly high-pressure games in the last nine days — including Saturday’s doubleheader in Cleveland — the offense was just sleepy on Wednesday night.

“We didn’t get a lot going,” Baldelli said. “Had a little opportunity in the first with a couple of walks. Had a chance there but really over the course of the game, it kind of shows you a little bit that sometimes those bullpen days can be definitely challenging to deal with. We had our chances, we had some good pitches to hit. The at-bats were probably just OK today. It wasn’t our best offensive night. That’s definitely going to happen.

“Our offense has been really good this year. Consistently good and tonight was just one of those nights.”

The Twins didn’t get their first hit until the sixth inning, when Jorge Polanco socked a clean single in front of Garcia in the sixth. Nelson Cruz followed with a walk and Eddie Rosario singled home Polanco, and after Miguel Sano hit a fly ball to left, Jake Cave walked to load the bases. Tuesday night’s hero LaMonte Wade Jr. pinch-hit for Jonathan Schoop, but hit a broken-bat grounder to second to squash what was really the team’s only rally all night long.

With two outs in the eighth, Rosario hit a soaring drive off the fence in right. Garcia — who had moved from center to right a couple innings earlier — attempted to catch it on the fly and missed, but center fielder Adam Engel backed him up perfectly, and threw a strike to third base to nail Rosario for the final out.

“I don’t mind that play,” Baldelli said when asked about if he’d endorse the risk taken by Rosario. “Would I call it probably the right play? Maybe not, but he was making something happen. He hits the ball down the right-field line. He might not have seen the center fielder going over there to pick that ball up. He might have thought he was going in standing up for all I know.

“It was a great play by their center fielder to get over there and to make a pretty good throw to third base. Usually, in those situations you probably say with two outs, if you’re going to go, you probably make sure you’re standing up but it’s harder out on the field when making those decisions than it is where we’re sitting.

“It is what it is. That’s not the reason we lost the game. We lost the game because we just didn’t have the kind of at-bats that we really needed to have tonight and again, that’s going to happen.”

Baldelli also agreed with the notion that it was a really nice play by Engel, who had to throw to a moving target at third base as Moncada was not near the bag as the play was developing.

“He’s really throwing to a spot probably,” said Baldelli, who of course was a big-league outfielder for seven seasons. “I can’t speak having zero experience in the infield, but as an outfielder, you make throws based on where your peripheral vision or your sense of space out there tells you to make the throw. You’re not looking a lot of time at exactly where you’re throwing the ball, but it was a great play by him.

“He’s a good outfielder. He knows what he’s doing out there.”

Rosario’s double was it for the Twins offense, as they went 1-2-3 in the ninth against White Sox closer Alex Colome for his 28th save.

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Notes & Quotes