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Donald TrumpDonald John TrumpFamily immigration detention centers could be at capacity within days: report Trump likely to meet with Putin in July: report DOJ requests military lawyers to help prosecute immigration crimes: report MORE's campaign reached out to Ohio Gov. John Kasich in May with an offer to make him the "most powerful vice president in history," The New York Times reported Tuesday.

Trump's oldest son, Donald Trump Jr., reached out to a Kasich adviser after the Ohio governor ended his own Republican presidential campaign, promising that if he accepted the vice presidency, Kasich would be in charge of domestic and foreign policy.

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The adviser asked what Trump would be in charge of, the report said, and Trump Jr. responded: "Making America great again."

Kasich has refused to endorse Trump, the GOP's presidential nominee, for president, and won't speak at this week's Republican National Convention even though it's taking place in his home state.

He has said Trump shouldn't expect an endorsement anytime soon. 

"Unless I see a fundamental change in that approach, it’s really hard for me to do a merger," he said in May. 

Trump eventually tapped Indiana Gov. Mike PenceMichael (Mike) Richard PenceHollywood goes low when it takes on Trump 'Queer Eye' star recounts his visit to White House Pence knocks Sherrod Brown in Ohio, boosts Renacci MORE to be his running mate, announcing his decision last week.