President Donald Trump's adviser Kellyanne Conway is believed to be behind leaks to the media designed to make White House press secretary Sean Spicer look bad, five sources reportedly tell CNN.

In a bylined story on the news network's website, senior reporter Dylan Byers writes:

"Though they offer no hard evidence, they say Conway is trying to offload blame for administration setbacks on Spicer to prove she is the more effective public advocate and earn a lasting place in the President's inner circle."

Byers writes the two appear to be locked in a Cold War.

"She's clearly guiding a press narrative that he's not up for the job, and that they're reviewing other candidates," he quotes a GOP strategist as saying. "It's becoming abundantly clear that Kellyanne is making Sean's job impossible."

And the story notes both Spicer and Conway have issued "no-so-indirect slights" at one another in recent days.

When Spicer was asked about Conway plugging Ivanka Trump's clothing line during one of her television appearances, he replied curtly answered: "She's been counseled."

After Trump backed Conway, she tweeted the president "likes counselor" more than "counseled," the story says.

"That was the first open shot," a source reportedly told Byers.

Spicer and Conway later gave conflicting views about the resignation of Michel Flynn as national security adviser, according to Byers.

But Conway denies being behind any leaks about Spicer.

"Absolutely not," she told Byers. "It's absolutely false. Sean has my full support, but most importantly, he has the president's full support. We work as a team."

Conway claimed she was offered the press secretary role "within an hour of the president winning" and turned it down, so why would she try to undermine him now?" according to Byers.

"Sean's doing a great job with impossible odds," Conway said. "He's got a tenacity and focus that's going to serve him well long term."