Yes, it’s possible President Donald Trump had his phone calls intercepted, stored and searched by U.S. spy agencies during the Obama administration, experts say -- but not necessarily in the way the president claims.

In a series of Saturday morning tweets, Trump accused his predecessor Barack Obama of tapping “my phones” in Trump Tower “just before the victory." He made the claim with one typo and no evidence, and the basis remains murky.

News organizations have been unable to confirm any judge-approved wiretapping, and there’s a widespread belief Trump sourced his claim using potentially unreliable articles, continuing a habit of making shocking and thinly sourced claims on Twitter.

Many experts have stated in television interviews that just two methods exist for wiretapping -- a “Title III” criminal warrant or an intelligence court order -- and that since the post-Watergate reforms of the '70s the president has been unable to order taps.

But presidential adviser Kellyanne Conway on Monday said Trump "has information and intelligence that the rest of us do not” and alternative paths do exist for recorded Trump calls -- should any exist -- to come into spy agency possession.

One potential path is through “incidental” collection in dragnet or targeted surveillance of foreigners, followed by warrantless “backdoor” searches.

Such “backdoor” searches could affect many Americans, not just Trump.

“'Wiretap' has both a specific legal definition and a generic definition,” says former National Security Agency senior executive Thomas Drake, who left the agency in 2007 amid an ultimately unsuccessful leak prosecution.

Drake, an internal critic of wasteful spending turned public advocate for privacy rights, went on a Twitter spree of his own on Monday, criticizing "evidence-free or fact-shallow analyses" of surveillance operations from "self-appointed [and] so-called experts."

“There exist 'other' secret executive authorities,” Drake says.

One such authority, Executive Order 12333, governs U.S. intelligence operations overseas and reportedly has been used to intercept, record and store every cellphone call in the Bahamas and Afghanistan.

Critics of the order view it as a potential blank check for spies to evade congressional or judicial review of actions that could harm Americans’ privacy. But intelligence officials have described the Constitution as having geographical limits at the U.S. border and say the 1981 order actually is a voluntary check on otherwise unrestrained presidential power.

Drake says the executive order "is a convenient backstop" for bulk collection that would be constitutionally problematic if conducted inside U.S. national borders under the Foreign Intelligence Surveillance Act.

Former high-ranking NSA official Bill Binney, who left the agency after more than 30 years in 2001, says EO 12333 allows for interception of American phone calls, citing both his experience at the agency and his understanding of the executive order.

“It’s all done by Executive Order 12333 and it’s done with the cooperation of the telecommunications companies," Binney said in a Fox News appearance Tuesday morning.

Georgetown University law professor Laura Donohue, an expert in surveillance policy, says, however, that even the theoretical collection of Trump’s communications under the executive order would not make his tweeted statements accurate.

On Twitter, Trump specifically accused Obama of ordering the tapping of his phones in New York’s Trump Tower. “Bad (or sick) guy,” he wrote.

“The key is where the intercept occurs. In the case of Trump Tower, if the intercept is on U.S. soil, then it would have to be some form of [Foreign Intelligence Surveillance Act authority],” Donohue says.

A “backdoor” search of records collected under EO 12333 may be possible, she says, but from her reading of Trump’s tweets “that doesn’t sound like what this is.”

Terrible! Just found out that Obama had my "wires tapped" in Trump Tower just before the victory. Nothing found. This is McCarthyism! — Donald J. Trump (@realDonaldTrump) March 4, 2017

Is it legal for a sitting President to be "wire tapping" a race for president prior to an election? Turned down by court earlier. A NEW LOW! — Donald J. Trump (@realDonaldTrump) March 4, 2017

I'd bet a good lawyer could make a great case out of the fact that President Obama was tapping my phones in October, just prior to Election! — Donald J. Trump (@realDonaldTrump) March 4, 2017

How low has President Obama gone to tapp my phones during the very sacred election process. This is Nixon/Watergate. Bad (or sick) guy! — Donald J. Trump (@realDonaldTrump) March 4, 2017

If records are collected within the U.S., surveillance operations targeting suspected terrorists or foreign intelligence targets is done under the FISA. One potentially relevant program under that law -- Upstream collection under the Section 702 of FISA -- takes data directly from the internet’s backbone.

"Upstream collection also includes telephone calls in addition to Internet communications," the Privacy and Civil Liberties Oversight Board, a government entity, reported in a review of Section 702 programs.

"The communications of U.S. persons can be acquired when a U.S. person is in contact with a foreign target (who need not be involved in wrongdoing in order to be targeted), when the government makes a mistake, and in certain other situations," the board wrote. "The government’s ability to query its databases for the communications of specific U.S. persons, and to retain and disseminate such communications under certain circumstances, heightens the potential for privacy intrusions."

Elizabeth Goitein, a surveillance law expert at New York University’s Brennan Center for Justice, says “backdoor” searches of records collected overseas under Executive Order 12333 or domestically under FISA currently are allowed.

"Under both FISA and 12333," she says, "Americans’ communications can be 'incidentally' intercepted by NSA. Under FISA, the raw data can be disseminated to CIA and FBI. That is now also true for EO 12333, but wasn’t true at the time the surveillance at issue here allegedly happened; however, even under EO 12333, NSA was allowed to share data about Americans if it was evidence of a crime or necessary to understand foreign intelligence."

The Obama administration relaxed rules for access to 12333 intercepts among agencies during its final days in office. Though members of Obama’s team reportedly took steps to widely distribute intelligence they deemed significant to Russian involvement in the election, that particular change had been in the works for years.

Goitein says, however, that she doubts Trump was referring to this type of interception and search.

“In defending the claim, the White House has pointed to articles that specifically discuss FISA Court applications, which as you know don’t play any role in EO 12333 surveillance,” she says.

The Guardian reported that authorities sought FISA surveillance orders covering four Trump associates in mid-2016, but the court reportedly turned them down, before authorizing surveillance of two Russian banks in October, according to a BBC report.

Goitein says that searching EO 12333 intercepts for U.S. person information is more difficult than for FISA, with "a high-level internal determination of probable cause" needed that the American is a foreign agent, whereas backdoor FISA searches require only a belief the search would return foreign intelligence or evidence of a crime.

But Executive Order 12333 protections are not laws, they are policies, and could theoretically be ordered changed by a president.

"I imagine he’d run into constitutional problems – that is, assuming anyone found out and had standing to challenge the surveillance," Goitein says.

But still, the scenario is possible.

Cato Institute scholar Julian Sanchez, who has written skeptical analysis of Trump’s claims for Just Security and Cato’s blog, says nonetheless "it’s a practical certainty" that some communications of Trump associates were captured by the government.

"An enormous number of conversations between Americans—including political figures of both parties—and foreigners are caught up in that way," he says. "But that wouldn’t require any nefarious interference by Barack Obama; it’s a wholly predictable side effect of how NSA does business."

Sanchez says incidental Section 702 intercepts may see "minimization" procedures limiting use of records collected on Americans, but that there exists "a potential 12333 loophole."

"Bulk collection under 12333 doesn’t run afoul of the prohibition on intentional targeting of U.S. persons," he says. "And the minimization rules applicable there aren’t statutory — they’re a matter of executive order and internal policy guidelines that, in theory, the president could countermand. How much practical pushback he’d get might come down to the personnel at the wheel when the request came in."

A White House spokesman did not directly respond to a request for comment on whether Trump will declassify any evidence that exists.

"The statement Sunday speaks for itself," White House Press Secretary Sean Spicer says in an email, referring to a three-sentence statement requesting a congressional investigation.

Obama and former officials in his administration have denied Trump’s charge.