Cleveland (CNN) John Kasich may be the most intensely courted man in the Buckeye State.

With just seven days until the GOP convention, the quest to convince Kasich to back Donald Trump -- or even participate in the convention he campaigned to bring to Cleveland -- has been quiet but feverish.

RNC Chairman Reince Priebus has pressed Kasich allies, even promising that donors will spring to aid Kasich's future endeavors if he cooperates now. Trump's top aide, Paul Manafort, has touted their increasingly professional campaign operation in the hopes of winning over the Ohio governor. Even vice presidential hopeful Newt Gingrich is joining the mix, lobbing a last minute plea to Kasich's team to get the governor to back Trump.

"The convention is a natural showcase for Republicans uniting behind the Trump campaign," said Ed Brookover, a Trump adviser. "The RNC and the campaign have been working very hard at bringing the forces together and showing that we're united in defeating Hillary Clinton."

Concerted effort

The push is part of a concerted effort by Trump allies and the RNC to move beyond an ugly GOP primary marred by personal insults -- and capped off with a victory by one of the most unpopular presumptive presidential nominees in modern history.

Four out of the last five Republican nominees are skipping the upcoming GOP convention, along with a number of members of Congress and rising stars in the Republican Party.

Even though Kasich still has no plans to set foot inside the arena, he'll still be a visible presence next week. He's scheduled to appear at nearly 20 events around town.

"He will have a robust schedule outside the convention hall," said Kasich spokesman Chris Schrimpf. "He is focused on supporting Senate, House and other down ballot candidates."

"Nobody's in the position they wanted to be in. No one," added one Kasich adviser, who pegged the odds of him appearing at the convention "somewhere between zilch and zero."

Determined not to let the no-shows undermine the big display of unity, GOP officials set out to at least slap a bandage on wounds that aren't quite healed.

Last Wednesday, Texas Sen. Ted Cruz, Priebus and their aides sat down to do dinner at Capital Grille in Washington. Priebus came with an agenda: What would it take to get Cruz to Cleveland?

Until that point there had been no discussions about Cruz speaking at the convention, according to a Cruz adviser. One of Trump's last-standing rivals, Cruz hasn't endorsed the presumptive GOP nominee. But he agreed to meet with Trump while he was in Washington the following day.

Trump did most of the talking.

"It was stream of consciousness like everything else he does," the Cruz adviser said. "He said 'I'd like to have you speak,' and he did pause long enough for Ted to say 'I'll be happy to.'"

In an interview with conservative radio host Glenn Beck, Cruz said he wanted to speak in Cleveland in part to address his nearly 600 delegates and grassroots supporters.

"There are patriots across this country who poured their heart and soul and blood and energy into this campaign," Cruz said. "I'm going to be there to say thank you and to do my very best to lay out a vision for what we as Americans, what we as conservatives believe, and where we go forward from here."

Chips falling into place

In recent days, more chips have fallen into place. House Speaker Paul Ryan, who has made a habit of publicly airing his disagreements with Trump, agreed to speak at the GOP convention after days of discussions with the Trump campaign and the RNC. Wisconsin Gov. Scott Walker, who's also been vocal in his criticism of Trump, pledged to support the nominee and said he would speak at the convention.

And while Florida Sen. Marco Rubio said he's skipping the confab -- and advisers on both sides said he was never offered a speaking slot -- he agreed to campaign with Trump after overtures from Manafort. The planned Miami event was ultimately cancelled in the wake of the Dallas shootings, but the Trump campaign took it as a positive sign that Rubio was open to appearing with the presumptive nominee.

But the man who's been the subject of perhaps the most intense lobbying effort still won't budge.

As convention aides out and about in Cleveland buzzed over the odds of the Ohio governor having a last-minute change of heart, and wondered whether the Ohio delegation might be punished with less-than-ideal seating on the convention floor, Kasich downplayed his odds of appearing.

"If I'm going to show up at the convention, and I'm not going to be saying all these great things about the host then I think it's inappropriate," Kasich said in a recent interview with WEWS NewsChannel 5 in Ohio. "I don't think that's the right thing to do, it doesn't feel right to me inside."

Publicly, Trump has shrugged off such snubs, at one point suggesting he wouldn't welcome anyone to speak at the convention who hasn't endorsed him anyway.

A spokesman for the Trump campaign declined to comment on its Kasich outreach.

But privately, Trump allies have spent weeks trying to press the Ohio governor to back Trump -- or at a minimum, participate in the convention.

Manafort, still holding out hope of an endorsement, recently reached out to Kasich's strategist, John Weaver, to brief him on efforts to run the campaign as a more disciplined and polished operation, according to people familiar with the discussions. Kasich's camp was unmoved.

Another overture arrived Sunday afternoon from Gingrich, an ally in their shared House days during the 1980s and 1990s. He asked Kasich's team whether the governor could be persuaded to endorse Trump or whether it was "a waste of time."

Priebus

Meanwhile, Priebus has been trying to convince Kasich to speak or appear at the convention, even if he won't endorse. The RNC chair tried reaching out to Kasich directly. But the Ohio governor, still aggrieved by Priebus's tweet after the Indiana primary declaring Trump the nominee, hasn't been receptive.

In a brief conversation between the two men, Kasich shunted Priebus to his chief of staff, Beth Hansen. That set off an unproductive game of phone tag between the two of them, according to two people familiar with the conversations.

But Priebus was also working through back channels, attempting to woo Kasich allies at the Ohio GOP. He even suggested he would help open a floodgate of donors for whatever political pursuit Kasich takes on next -- if only Kasich would play nice and participate in the convention, according to someone familiar with the conversation.

"Ohio is a battleground state," Sean Spicer, the RNC's chief strategist and communications director, said by way of explanation.

In recent days, the channels between the Kasich camp and Trump allies have grown more strained amid worries that Kasich's team could be supporting efforts to unbind the delegates. Privately, Kasich aides assured the Trump campaign and others that they have no plans to disrupt the convention.

But it's just another indication the GOP primary wounds are far from healed. In an interview with The Washington Post published this week, Kasich didn't hold back his sour feelings toward the RNC chief.

"What Priebus did was dead wrong, after Indiana, declaring Trump the nominee," Kasich said. "It was amateur hour for him."