New York Yankees owner Hal Steinbrenner realizes there is a chance the price may be going up to sign Aaron Judge to a long-term contract after the star slugger’s outstanding first half.

Judge, eligible for free agency after the World Series, leads the major leagues with 29 homers. He is second in the AL with 60 RBIs and is batting .281, a big reason the Yankees began Wednesday with a major league-best 58-23 record and a 13-game lead in the AL East.

“Aaron is a great Yankee and he’s very valuable to this organization,” Steinbrenner said. “He’s a great leader. Obviously, he’s performed extremely well this year, which we’re all thrilled about. So, look, any great Yankee, yes, it’s something we’re going to be looking at and talking about seriously. It means a lot to the organization. Nobody’s going to deny that.”

Judge turned down an eight-year contract worth $230.5 million to $234.5 million, cutting off talks ahead of the April 8 opener and saying he wouldn’t negotiate again until after the season.

After the Yankees made their long-term offer public in April, Judge and the team agreed last month to a $19 million, one-year deal that avoided an arbitration hearing. Steinbrenner said even if talks do resume during the season, the team wouldn’t publicly discuss negotiations until after the Yankees’ season is over.

“We made an offer that I feel was a very good one,” Steinbrenner said. “It was based on the numbers, of course, but it was also based in part as what he means to this organization. It was a combination of both. And we just didn’t get a deal done. We had less time, of course, this offseason than we would normally because of lockout and all. But there’s no regrets. We’re going to be having discussions at some point.”

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WEDNESDAY’S GAMES

BLUE JAYS 2, ATHLETICS 1: Bo Bichette hit a tiebreaking solo home run in the eighth inning as Toronto snapped a five-game losing streak with a win at Oakland.

Toronto’s Matt Chapman also homered against his former team for the second straight day. Ramón Laureano homered for the A’s, who failed to complete their first sweep of the season.

Blue Jays starter José Berríos pitched six strong innings, allowing one run on four hits with six strikeouts and a walk. Adam Cimber (8-2) followed with two perfect frames to earn his eighth win, most among major-league relievers.

TIGERS 8, GUARDIANS 2: Miguel Cabrera had three RBI at Detroit to help the Tigers complete a four-game sweep against Cleveland for the first time since 2013.

Tigers’ pitcher Michael Pineda (2-3) allowed two runs and five hits over five innings, then four teammates combined to pitch four innings of scoreless relief.

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Cleveland’s Shane Bieber (4-4) gave up five runs on seven hits and three walks while striking out six over 5 2/3 innings.

WHITE SOX 9, TWINS 8: Andrew Vaughn tied the game with a two-run homer in the eighth inning, and Leury Garcia hit a RBI single in the 10th to give Chicago a walk-off victory over Minnesota.

The White Sox trailed five times in the game and tied it each time before taking their first and only lead in extra innings to avoid a three-game sweep. Chicago snapped a seven-game losing streak to the AL Central-leading Twins.

Playing his first game since April 23, Eloy Jiménez made an immediate impact for the White Sox, hitting a two-run homer in the fourth inning and an RBI single in the seventh to tie the game at 6-6. Jiménez had been sidelined with a torn tendon in his left hamstring. He also made a difficult catch before running into the netting down the left-field line to end the sixth.

Jorge Polanco homered twice for Minnesota.

CUBS 2, BREWERS 1: P.J. Higgins hit a tiebreaking two-out double off Josh Hader in the ninth inning, as Chicago rallied to win at Milwaukee.

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After Brewers starter Corbin Burnes threw seven shutout innings, the Cubs broke through against Milwaukee’s bullpen by scoring in each of the last two frames. The Cubs took two of three at Milwaukee and have followed a 10-game losing streak by winning four straight series.

David Robertson retired the side in order in the ninth for his 12th save in 16 opportunities.

Earlier in the day, Cubs right-hander Kyle Hendricks was placed on the injured list after leaving his Tuesday night start early because of soreness in his throwing shoulder. The 32-year-old Hendricks is 4-6 with a 4.80 ERA this season.

PLAYERS’ UNION: Bruce Meyer, 61, was promoted to deputy executive director of the Major League Baseball Players Association after leading the union’s negotiations during a 99-day lockout that ended in March.