Efforts to draft a third-party candidate are under way and while no possible contender has agreed, several are open to being approached, CBS News has learned.

One individual involved in the process tells CBS News the next three to four weeks are critical to figuring out if launching an independent bid is realistic. This individual cautioned, however, that efforts are disparate. Whether or not it's possible organizationally -- as well as the mechanics of such an operation -- are still up in the air.

First reported by the Washington Post, GOP operatives trying to derail Donald Trump by bringing in another conservative candidate have started considering several names, including former Oklahoma Sen. Tom Coburn, former Secretary of State Condoleezza Rice and retired Army Gen. Stanley A. McChrystal. Star of the reality television show "Shark Tank" and billionaire investor Mark Cuban was floated as a possibility, but he told the Post, "I don't see it happening. there isn't enough time," although he also said that Trump "knows I would put him in his place."

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While nobody has shut the door to Sen. Ben Sasse, an outspoken Trump critic, the Nebraska Republican is deemed unlikely -- and is at least far less likely than Ohio Gov. John Kasich, who dropped out of the Republican primary contest nearly two weeks ago.

Retired Marine Corps. Gen. James Mattis had been seriously considering in the spring, the source confirmed. But he also ruled out a presidential bid.

Other names are in the mix, according to the source. Republicans' 2012 presidential nominee Mitt Romney, however, is considered to be a long-shot.

The individual said donors have been very receptive -- if there's a real candidate -- but declined to give names of possible financiers.

The price tag is said to be north of $100 million, though not much more than that. Organizers figure that the nature of this kind of campaign wouldn't require the force of a $1 billion race: Rather, it would be targeted, wouldn't play every battleground state. It would pin its hopes, instead, on earned media, attention from debates, and some paid advertising.

Among the challenges these avid opponents of Trump face over the next few weeks is ballot access. They consulted advisers to former New York City mayor Michael Bloomberg, who shut the door on his own third-party bid in March, to devise their own strategy, but time is growing short. Texas' deadline has already passed and North Carolina's is looming.

Another hurdle to overcome: other Republican party leaders.

Earlier Sunday, Republican National Committee Chair Reince Priebus told CBS' "Face the Nation" that the attempts to draft a third-party candidate are a "suicide mission" for GOP operatives and advising against them.

"I think what people should do is take the Paul Ryan approach which is to work with Donald Trump and find out whether or not there's common ground ... as opposed to blowing everything up," Priebus said in an interview.