But Trump's demand, which followed his unsubstantiated claim that an informant had been "implanted, for political purposes" into his campaign, goes even further, Vladeck said.
"In this context, it's not just a political decision. It's a political decision to investigate the people that are investigating him," Vladeck said in an interview. "Even if it was ever appropriate, this seems to be the single least-appropriate instance."
Eric Columbus, who was senior counsel to deputy attorneys general during the Obama administration from 2009 to 2014, agreed with Vladeck's assessment of Trump's demand.
"It's not normal," Columbus said. "I'm hard-pressed to think of instances before this presidency where the president informs the Department of Justice to do something so specific."
On Friday, The New York Times, citing people familiar with the matter, reported that the alleged FBI informant was sent to talk to some of candidate Trump's campaign advisors, including former policy aides Carter Page and George Papadopoulos. The informant also looked into other campaign associates such as Michael Flynn, who would become Trump's first national security advisor, and former campaign chief Paul Manafort, the Times reported.
Trump tweeted earlier Friday that if the reports of an informant in his campaign are true, it would constitute the "all time biggest political scandal!"
Two days later, the president took to Twitter to demand an investigation into whether his campaign had been monitored "for political purposes."
By Sunday evening, the Justice Department confirmed that it had referred the matter to Inspector General Michael Horowitz, folding Trump's demanded inquiry into a probe of the FBI's acquisition of warrants to monitor Page during the campaign.
"The Department has asked the Inspector General to expand the ongoing review of the FISA [Foreign Intelligence Surveillance Act] application process to include determining whether there was any impropriety or political motivation in how the FBI conducted its counterintelligence investigation of persons suspected of involvement with the Russian agents who interfered in the 2016 presidential election," a Justice Department representative told CNBC.
ABC News, meanwhile, reported that Deputy Attorney General Rod Rosenstein and FBI Director Christopher Wray would head to the White House on Monday afternoon. The president's demand would be part of the conversation, according to ABC.
NBC News confirmed that Trump would indeed meet with the two law enforcement officials, although a White House representative said that the meeting was scheduled before the president's weekend tweets.
The White House did not immediately respond to CNBC's request for comment.