GOP 2016 Cleveland

Ohio Gov. John Kasich speaks at the The Rock and Roll Hall of Fame and Museum on Tuesday, July 19, 2016, in Cleveland.

(Alex Brandon, The Associated Press)

CLEVELAND, Ohio -- There's a new wrinkle in this week's ongoing saga between Republican presidential nominee Donald Trump and Ohio Gov. John Kasich.

Kasich, the New York Times Magazine reported Wednesday, rejected feelers to join Trump's ticket and a chance to be "the most powerful vice president in history."

Donald Trump Jr. broached the idea with an unidentified senior Kasich adviser in May and suggested the governor could oversee domestic and foreign policy, according to the magazine. Asked what duties his father would have, Trump Jr. reportedly replied "casually" by invoking the campaign's "Make America Great Again" slogan.

Two operatives close to Kasich's political team confirmed the account to cleveland.com on the condition they not be identified. Representatives from the Trump campaign did not respond to a request for comment.

Trump took to Twitter later in the day to deny that he offered Kasich the job.

John Kasich was never asked by me to be V.P. Just arrived in Cleveland - will be a great two days! — Donald J. Trump (@realDonaldTrump) July 20, 2016

The news comes on the day Trump's eventual choice for the vice presidency, Indiana Gov. Mike Pence, will accept his nomination at the Republican National Convention in Cleveland. It also comes in the middle of a very public fight between the Trump and Kasich camps as a fractured party tries to unite for the general election.

Kasich, who staged an unsuccessful White House bid this year, is not speaking at the convention and has refused to endorse Trump, citing the New York businessman's divisive tone. He long ago ruled out a spot on Trump's ticket and has said repeatedly that he is unsure he and Trump will ever resolve their differences.

But the Trump team arrived in Cleveland this week determined to antagonize Kasich in his home state. On Monday, top Trump adviser Paul Manafort called Kasich an embarrassment to Ohio, enraging the governor's loyalists and ignoring his high job-approval ratings. Trump called into Fox News Channel that night -- cutting into his prime-time convention programming -- to escalate the feud.

Meanwhile, many members of Ohio's convention delegation -- 66 party insiders devoted to Kasich -- are unhappy with their seats on the floor of Quicken Loans Arena. They also are angry about how the RNC handled a video that paid tribute to late Ohio GOP Chairman Bob Bennett and late Sen. George Voinovich.

Then on Tuesday, Kasich appeared to mock Trump by arriving at an Ohio delegation gathering on an escalator, a scene reminiscent of Trump's theatrical campaign kickoff.

Kasich met with New Hampshire delegates Wednesday afternoon in Cleveland's Little Italy neighborhood. He finished second to Trump in the state's critical primary and might be planting seeds for another run for president.

One of Trump's New Hampshire allies called on the delegates to boycott the event. Kasich arrived to a decent-sized crowd of roughly 45. But when he asked who among them wasn't from New Hampshire, many raised their hands.