CNN has reached out to the White House for comment.
His alleged snubbing is the latest development in the tug-of-war for influence over Trump's White House between firebrands such as Bolton and those who have taken a more moderate approach to foreign policy, such as Secretary of State Rex Tillerson and Defense Secretary James Mattis.
Bolton's op-ed comes days after Sebastian Gorka, who advocated a hawkish stance against terrorism, left his position as a White House adviser.
Chief of staff John Kelly, who assumed the role in late July, has been conducting a review of the West Wing that includes assessing individual staffers' portfolios.
Bolton says Iran deal a threat to US
In a memo drawn up after a July directive from Steve Bannon, the recently ousted White House chief strategist, Bolton pushes for selling the idea of leaving the Iran deal to the public in a "white paper" and lays out a strategy for the "campaign" and its "execution."
Bolton has been frustrated at the rise of more traditional foreign policy thinkers within the White House, such as Mattis and Tillerson, who have favored remaining in the deal. The agreement curbs Iran's nuclear weapons program in exchange for the lifting of sanctions. Iran remains under multiple sanctions for terrorism-related activities.
"Trump can and should free America from this execrable deal at the earliest opportunity," Bolton writes.
Where proponents of the deal, including lawmakers and former Obama administration officials, see the pact as a way to get visibility on Iran's nuclear activities, and, at least for the time being, stop it's nuclear program, Bolton sees only danger.
"The JCPOA is a threat to US national-security interests, growing more serious by the day," Bolton writes, though he doesn't offer evidence. "If the President decides to abrogate the JCPOA, a comprehensive plan must be developed and executed to build domestic and international support for the new policy."
His memo, he says, fills that function. "It is only five pages long, but like instant coffee, it can be readily expanded to a comprehensive, 100-page playbook if the administration were to decide to leave the Iran agreement," Bolton writes.
He adds that there is no need to wait for the next deadline in October, when the US must next certify that Iran is sticking to the deal.
The Joint Comprehensive Plan of Action, known as the JCPOA, was an international agreement hammered out over 20 arduous months of negotiations. China, France, Germany, Russia, the UK, the US, the EU and Iran reached a deal in July 2015 and it was implemented in January 2016.
The UN's International Atomic Energy Agency has regular access to nuclear sites inside Iran and verifies that it is implementing its side of the deal; in exchange, the US, UN and EU lifted nuclear related sanctions. Every 90 days, the US president must certify that Iran is keeping up its end of the deal.
Trump campaigned against the deal and continues to criticize it, but because Iran is complying, he has certified it twice on the advice of his national security staff. But officials in his administration have clearly been looking for ways to find wiggle room to get out of the deal.
Some, like US Ambassador to the UN Nikki Haley, have used the line that Iran is not complying with the "spirit" of the deal, pointing to Tehran's activities in the region, including its support for Houthi rebels in Yemen and its backing of Syrian President Bashar al-Assad.
Bolton says that Trump can bolster his case for abrogating the deal "by providing new, declassified information on Iran's unacceptable behavior around the world."
These activities, though, are not part of the JCPOA, deliberately left as a separate issue by the Obama administration and the other international negotiators, who said that to include every single gripe with Iran would make negotiations too unwieldy to resolve.
Some proponents of the deal, watching the Trump administration's moves, are already campaigning to keep it. They point to the security consequences of an Iran without constraints on its nuclear weapons program and to the economic fallout as European and Asian firms would likely continue to do business with Tehran while US firms are shut out.
"Accordingly," Bolton writes, "we must explain the grave threat to the US and our allies, particularly Israel." But many in Israel's security establishment argue for keeping the deal in place, and making sure its implementation is as rigorous as possible.
Bolton makes the case for a four-step campaign that begins with "early, quiet consultations with key players such as the UK, France, Germany, Israel and Saudi Arabia, to tell them we are going to abrogate the deal based on outright violations and other unacceptable Iranian behavior, and seek their input."
That would be followed by a detailed white paper that includes declassified intelligence explaining why the deal hurts US security interests; a diplomatic campaign against the deal, especially in Europe and the Middle East; and efforts to sway lawmakers and the public to build support.
Eventually, the US should move on to recreating a new coalition "to replace the one squandered by the previous administration, including our European allies, Israel and the Gulf states," Bolton writes.
Russia and China, both of which are closer to Iran, "obviously warrant careful attention in the post announcement campaign," Bolton writes. They should only be told just before the announcement to leave, he writes. "We should welcome their full engagement to eliminate these threats, but we will move ahead with or without them."