"It doesn't happen at all," Aki Peritz, former CIA counter-terrorism analyst, told BBC Radio 4. "If the President is to be believed, Barack Obama had done something that is completely out of character and has not been done since the 1970s, and even then that caused all kind of scandal during the Nixon years."
Mr Peritz said Mr Obama, who is a constitutional lawyer, "would never do this".
Over the weekend, FBI director James Comey argued the claim must be corrected by the Justice Department because it falsely insinuates the FBI broke the law.
White House press secretary Sean Spicer called for the US Congress to investigate Mr Trump's claim, which he said was based on "very troubling" reports "concerning potentially politically motivated investigations immediately ahead of the 2016 election".
Mr Spicer said the White House wants the congressional committees to "exercise their oversight authority to determine whether executive branch investigative powers were abused in 2016".
Despite the severity of his claim, Mr Trump did not provide any evidence Mr Obama was responsible for surveillance at his property and has not provided any since.
Mr Peritz said: "When director Comey comes out and probably repudiates this accusation by the president, we've set up a very interesting uncharted place where you have one of our top law enforcement officials going up against the president."
When asked if it was a truly serious matter, he replied: "This could be a matter that brings down a president. It also could be nothing at all.
"The US government really has to do a very thorough investigation into the relationships, if they exist, between the Russian government, the Russian intelligence services and individuals in the Trump campaign during and after the campaign."
He also said: "If the FBI is actually surveilling individuals, it was probably legitimate legal targets such as the Russian ambassador or individuals in Moscow involved in the intelligence services and they in turn were talking to people.
"But the American citizens in New York city are not the actual targets unless they have been identified by the FBI as agents of a foreign power, or a terrorist."
Mr Obama has denied ever ordering the wiretapping of any US citizen and his spokesman Kevin Lewis said a “cardinal rule” of his administration was that “no White House official ever interfered with any independent investigation led by the Department of Justice”.
Former director of national intelligence James Clapper flatly denied the existence of an order to bug Mr Trump.