Media reports said the intelligence officials found the comment "so troubling" they went to the department's inspector general, the BBC reported on Friday.
In a tweet, Trump dismissed the claims as "fake news".
Democrats are trying to get the complaint turned over to Congress, with the details still unknown.
Only a few details about the complaint, which was filed on August 12, have been made public.
Intelligence Community Inspector General Michael Atkinson said the complaint consists of a "serious or flagrant problem, abuse or violation of the law" that involves classified information, a letter to lawmakers revealed.
It is not yet known who made the complaint, which foreign leader Trump was speaking to, what promise - if any - was made and whether Trump took any action as a result.
However, media reports suggest that at least part of the complaint related to Ukraine, citing officials with knowledge of the matter.
The acting director of national intelligence, Joseph Maguire, has so far refused to share any details of the complaint with lawmakers, leading to an outcry among Democrats.
Earlier this month, before the whistleblower's complaint came to light, House Democrats launched an investigation into Trump and his lawyer Rudy Giuliani's interactions with Ukraine.
Three Democratic panel heads - Eliot Engel (foreign affairs), Adam Schiff (intelligence) and Elijah Cummings (oversight) - said Trump and Giuliani had attempted "to manipulate the Ukrainian justice system to benefit the president's re-election campaign and target a possible political opponent".
They allege that Trump and Giuliani attempted to pressure the Ukrainian government into investigating former Vice President Joe Biden and his son Hunter Biden, who previously served on the board of an Ukrainian gas company.
Joe Biden is currently seeking the Democratic presidential nomination.
Trump and Ukrainian President Volodymyr Zelenskyy had a phone conversation on July 25, two and a half weeks before the complaint was filed.
On Thursday afternoon, Trump wrote on Twitter that he knew all his phone calls to foreign leaders were listened to by US agencies.
"Knowing all of this, is anybody dumb enough to believe that I would say something inappropriate with a foreign leader," he asked.
Meanwhile, Giuliani in an interview with CNN, has both confirmed and denied that he had asked Ukraine to investigate Joe Biden.
He explained the contradiction by saying that he had asked Ukraine "to look into the allegations that related to my client, which tangentially involved Joe Biden in a massive bribery scheme".
Trump and his fellow Republicans have questioned whether it represented a conflict of interest that Hunter Biden had served on the board of Burisma, an Ukrainian gas company.
In May, Ukraine's prosecutor general said there was no evidence of wrongdoing by Joe or Hunter Biden.
( With inputs from IANS )