CloutHub is one of several companies the Trump camp is considering, people familiar with the discussions say. Another is FreeSpace, a Facebook alternative. Its parent company, Skylab Apps Inc., promises customers—which range from CBD sellers to Promise Keepers, an evangelical Christian group—autonomous social-media networks that can’t easily be blocked or shut down.

It is possible another contender could emerge. The decision by Facebook’s independent oversight board on May 5 to uphold the company’s ban on Mr. Trump, at least for now, has added more urgency to the discussions, the people familiar with them say.

The former president is interested in being paid in exchange for the followers he would presumably bring to the new social networks, people familiar with the situation said. Mr. Trump had nearly 89 million Twitter followers.

“He’s not that interested in equity. He wants cash money up front, like a license fee,” said one person familiar with the process.

The talks are part of a broader effort on the right to build an infrastructure beyond the reach of Big Tech.

A group of conservative investors, including Dallas investor and former Trump adviser

Darren Blanton,

has been considering an investment in Rumble, a Toronto-based YouTube alternative that shot to prominence among right-leaning users in recent months, according to people familiar with the matter. Rumble went from fewer than one million monthly visits in August to nearly 58 million as of April, according to SimilarWeb. That is still a fraction of YouTube’s 6.2 billion monthly visits.

Mr. Trump and many other prominent figures on the right had their access to mainstream social-media platforms restricted after the Jan. 6 Capitol riot. The companies have said that false claims that the presidential election was stolen violate their policies, and that keeping Mr. Trump on the platforms risked further incitement of violence.

Mr. Trump now has a section of his website labeled “From the Desk of Donald J. Trump” filled with statements similar in substance to his now-defunct Twitter feed. The blog includes buttons that allow readers to share the statements on Twitter and Facebook.

A spokesman for Mr. Trump,

Jason Miller,

has said on Twitter that the blog is “not a new social media platform. We’ll have additional information coming on that front in the very near future.”

Mr. Trump has a rough target to unveil his new social-media plans by July 4, people familiar with the matter said. It is possible he could require multiple partners to replace the functionality of Facebook, Twitter and YouTube.

Building a social network with anywhere near the scale of Big Tech’s major platforms would be a major challenge. Some people close to the former president say it is unlikely Mr. Trump could draw as big a following on new platforms as he did on Twitter.

Mr. Trump and his team have held more than two dozen meetings on potential social-media plans, according to people familiar with the discussions. One of Mr. Trump’s primary objectives is to find what he has called an “indestructible platform” that can’t easily be taken down, according to people familiar with the former president’s remarks on the topic.

Another right-wing social-media platform, Parler, built a big following after the 2020 election, briefly becoming the most downloaded app in the country and racking up more than 15 million users. The Trump Organization held talks with Parler last year about potentially taking a stake in the company, according to people familiar with the matter. BuzzFeed was the first to report the talks.

Parler was stopped in its tracks in the wake of Jan. 6.

Apple Inc.

removed it from its app store while Amazon Web Services, which supplies remote computing capabilities to power companies’ websites, booted Parler over concerns that Parler wasn’t able to effectively moderate threats of violence on its platform.

Parler has since returned as a website. Its traffic has dropped from 20 million monthly visitors in January to 2.6 million in April, according to SimilarWeb. Apple has said it would lift the ban from the App Store.

The specter of the crackdown on Parler has loomed over the latest round of discussions to find platforms for Mr. Trump and other conservatives, people familiar with the discussions say. To have wide distribution, any app will have to abide by the terms of service of the major app stores.

Dean Grey, the chairman of Skylab, the Texas-based parent company of FreeSpace, which has met with Mr. Trump, said in an interview that his company’s products can provide the indestructibility the former president is seeking.

Skylab offers clients “an autonomous technological and financial ecosystem free from Big Tech and Wall Street,” according to an investor presentation reviewed by The Wall Street Journal. It includes a private cloud for powering web services, payment processing through independent banks, and its own ad network, Mr. Grey said.

The presentation said Skylab is “funded and founded by conservatives.” Mr. Grey said his technology, which has up to now appealed to people in industries worried about legal or regulatory risk, is in demand with conservatives worried about being “deplatformed” online.

“They want a platform, they want their own servers and they want their own banking,” Mr. Grey said. “Everyone now is just dealing with what people who were in the crypto or CBD industries have been dealing with for years.”

Skylab’s investor presentation said it had $2.6 million in revenue in 2020. It is trying to raise $25 million from friends and family at a valuation of about $100 million, according to the presentation. FreeSpace is still in a “beta phase,” Mr. Grey said, adding that Skylab is debt free.

Although Mr. Trump has met with representatives of Skylab’s FreeSpace social network, another possibility would be for him to buy or lease code from Skylab to create his own social-media network, according to people familiar with the matter.

CloutHub’s Mr. Brain said that his platform, which launched in 2019, is ideal for Mr. Trump’s purposes because it is specifically designed for civic debate. It includes an Instagram-like news feed with user posts, and a channel for YouTube-like online videos. Mr. Brain said he didn’t intend for the platform to cater to either side of the political aisle, but it has proven popular with conservatives.

Mr. Brain says he has “zero tolerance for hate” and uses an artificial-intelligence tool to keep hate speech off the platform. Amazon Web Services is one of his site’s vendors.

CloutHub has three million users, about 15 employees and is in the midst of raising a seed-funding round of $5 million, according to Mr. Brain.

—Sam Schechner contributed to this article.

Write to Keach Hagey at keach.hagey@wsj.com