The rumor was apparently being spread by some members of the European Union.

The White House is denying a report in the Wall Street Journal that said the administration would not withdraw from the Paris climate accord.

The Hill:

Multiple reports surfaced on Saturday saying the administration had appeared to soften its stance toward the deal. A top EU climate official told AFPthat the U.S. had signaled it was no longer planning to renegotiate the non-binding treaty. The Wall Street Journal also reportedthat President Trump was not planning to pull out of the deal. "The U.S. has stated that they will not renegotiate the Paris accord, but they will try to review the terms on which they could be engaged under this agreement,” said the EU's commissioner for climate action and energy, Miguel Arias Cañete, according to the Journal. Withdrawing was one of Trump’s key promises during his presidential campaign. In June, a newly elected Trump publicly rejected the deal, which he called “unfair at the highest level to the United States.” The initial decision to pull out was seen as a rebuke to the international community, which agreed on the treaty in 2015.

The EU official and other international climate bureaucrats quoted an administration official who said the US would seek to remain in the deal:

The denial came after the Wall Street Journal reported that a White House senior official, Everett Eissenstat, had told people at a meeting of energy ministers in Montreal that the administration may revise or craft a new climate deal and emissions standards rather than pull out altogether, according to a top European energy official cited by the Journal. As recently as early August, the White House signaled its intent to continue the process of withdrawal by delivering an official notice to the United Nations vis-à-vis the State Department. [...] An international official familiar with the meeting told POLITICO earlier Saturday that Eissenstat, the No. 2 official on the National Economic Council, told diplomats during a closed-door meeting that the U.S. was mulling plans to remain in the Paris deal and to rethink Obama's climate pledge. But White House officials strongly denied that. Another White House official said Saturday diplomats were mischaracterizing Eissenstat's comments. A second, non-U.S. attendee at this weekend's meeting also said Eissenstat's comments were being misconstrued. The attendee, who witnessed his comments in person, said Eissenstat simply reiterated the administration's existing position, which is that the U.S. will continue to engage in climate talks with an eye toward reaching a better deal. "He basically repeated exactly the State Department press release from August," the person said, referring to a recent statement from the department outlining its intention to eventually withdraw, but continue participating in Paris discussions. "This is being misreported. Unhelpfully so I think."

This appears to be wishful thinking on the part of EU officials rather than a signal that the Trump administration was about ready to change policy. They misconstrued Eissenstat's statement, perhaps hoping to put pressure on Trump to rethink his position.

If they accomplished anything, it was to put the Paris deal back in the news.

Trump wants more pressure put on China, the number one emitter of greenhouse gases in the world. As the Paris deal stands now, China's targets for emissions are ridiculously low. This puts US companies at a competitive disadvantage.

US emissions have been falling since 2006 - the result of the fracking revolution which has dumped massive amounts of cheap, cleaner burning natural gas on the market. In fact, market forces are doing a lot more to reduce emissions than any treaty every signed. There's a lesson there that the UN doesn't want to learn.