Trump is still "obsessed" with finding the person, though he is being counsel led by White House Chief of Staff John Kelly to let it pass, to avoid bringing more attention to the claims in the op-ed that shook the political world.
However, there were no details the identity of the individuals the White House aides have zeroed in on.
The op-ed published on Wednesday afternoon, just a day after excerpts from veteran journalist Bob Woodward's new book, "Fear: Trump in the White House", were published.
The anonymous writer said the resistance inside Trump's administration is not the same as the resistance from the political left.
The author wrote that the resistance inside the government wants "the administration to succeed ... But we believe our first duty is to this country, and the President continues to act in a manner that is detrimental to the health of our republic".
The author also wrote that the "root of the problem is the President's amorality" and assails Trump's "reckless decisions", "erratic behaviour" and what the official describes as the President's "impetuous, adversarial, petty and ineffective" leadership style.
More than 25 high-ranking Trump administration officials have come out publicly denying having penned the op-ed, including Vice President Mike Pence, Secretary of State Mike Pompeo, Director of National Intelligence Dan Coats and Defence Secretary James Mattis, CNN reported.
It was previously reported that White House aides were struggling on Thursday morning to get ahead of the op-ed as the Cabinet and other top officials were releasing their own statements, according to an administration official.
On Friday, Trump said he wants Attorney General Jeff Sessions to investigate and uncover the identity of the individual who authored the opinion piece.