Wednesday, Trump spoke of seeing photographs of "innocent people, including women, small children and even attractive little babies", who had died from the gas attack. Former Trump political adviser Roger Stone has accused Kushner of leaking unfavorable stories about Bannon.
And another White House official said Trump was in an "amazing mood".
Bannon and Priebus did not immediately respond to the Journal's requests for comment.
For now, Kushner has triumphed, with Trump evicting Bannon from the powerful National Security Council principals' committee that the ideologue had pretty much designed and ushered himself into. Various groups and spheres of influence have sought to gain the attention of the President, with power struggles resulting in an internal mess for the Trump administration.
Trump reverses himself on NATO, China, Russia and more
I said it was obsolete. "I like Steve, but you have to remember he was not involved in my campaign until very late", Trump said . Trump referred to the Syrian leader as a "butcher". "We may be at an all-time low", Trump said of US-Russia relations Wednesday.
Cohn, Kushner and Dina Powell, the deputy national security adviser, have been labeled the White House's "Democrats" by Bannon's allies, and the two sides have taken turns slinging anonymous arrows at each other in the press.
The former Trump advisers said Mr Kushner, husband of Mr Trump's daughter Ivanka Trump, is trying to tug the President into a more mainstream position, while Mr Bannon is trying to keep aflame the nationalist fervour.
"He's got a long fuse for that kind of thing", said one.
Bannon has dismissed stories about an impending departure as "100 percent nonsense".
Instead of leaning upon the nationalist worldview of Bannon - who has argued against USA intervention overseas and was a key architect of Trump's "America First" policy - Trump dove headfirst into a foreign conflict, ordering airstrikes in Syria to punish the regime of Bashar al-Assad for its use of chemical weapons on civilians.
New leak suggests NSA penetrated Mideast banking networks
You have encouraged us in our mission - to provide quality news and watchdog journalism. Repeated messages seeking clarification from EastNets went unreturned.
Asked by reporters Thursday whether his administration needed a shakeup, Trump said he was proud of what his staff had accomplished.
Bannon, a far-right Republican and former Brietbart News executive, has been at odds with Kushner, a former real estate developer and Democratic donor.
Trump ordered airstrikes against Syrian targets that drew praise in many parts of the world and staged an error-free summit with Chinese President Xi Jinping, complete with his wife, Melania, wearing a red dress to symbolise the colour of the Chinese flag.
Bannon's faction has come to term Cohn as "Globalist Gary", an insult for those aligned with the Bannon's populist views.
"We've had a tremendous success", he told reporters on Air Force One. Bannon has told confidantes that he believes Kushner's contact with Russians, and his expected testimony before Congress on the subject, will become a major distraction for the White House.
Simple Moving Average Analysis of Regions Financial Corporation (RF)
Enterprise Financial Services Corp decreased Enterprise Financial Service (EFSC) stake by 9.47% reported in 2016Q4 SEC filing. The company reported $0.34 earnings per share (EPS) for the quarter, missing the consensus estimate of $0.36 by $0.02.