The president reportedly made the requests shortly after then-FBI Director James Comey told lawmakers the agency was investigating possible coordination between Russian interests and Trump aides during the election.
"I don't know whether such collusion existed".
Reports say that the White House has however denied the allegation.
The Washington Post reported Monday, and other news outlets later confirmed, that Trump had asked Coats and Rogers in March to push back publicly against an FBI investigation into his campaign's ties to Russian Federation.
Coats later said that he does not dispute the validity of ongoing Russian Federation investigations, saying the probes "are in place to get us to the right conclusion with a known result", so the country can move on to other issues.More news: Trump reacts to Manchester attack as overseas trip continues
Coats and Rogers refused to comply with the requests, which they both deemed to be inappropriate, according to two current and two former officials, who spoke on the condition of anonymity to discuss private communications with the president.
While Coats testified before the Senate, the man who led the Central Intelligence Agency during last year's presidential campaign, John Brennan, told a House panel he saw information indicating contacts between Russian officials and members of the campaign.
The White House issued a statement on the hearings, saying: "This morning's hearings back up what we've been saying all along: that despite a year of investigation, there is still no evidence of any Russia-Trump campaign collusion, that the President never jeopardized intelligence sources or sharing, and that even Obama's CIA Director believes the leaks of classified information are "appalling" and the culprits must be 'tracked down'". "It raised questions in my mind about whether Russian Federation was able to gain the cooperation of those individuals".
FBI chief Mr Comey's dismissal was greeted with reactions, with critics accusing the president of trying to thwart the FBI investigation into Russia's alleged interference in the U.S. election and any Moscow ties to Trump associates.
It is unclear if a similar memo was prepared by the Office of the Director of National Intelligence to document Trump's conversation with Coats.More news: Pak mulls new legal team to fight Jadhav case in ICJ
Forty-eight percent of those polled said they oppose Trump's decision to fire Comey compared to 37 percent who supported the president's decision while 15 percent remain unsure.
In response to the report, a White House official pointed out that acting FBI director Andrew McCabe had testified last week that there had been "no effort to impede our investigation to date".
"Any political shaping of that presentation or intelligence would not be appropriate", he said.
He said that he would cooperate with the Russian Federation probe, now being led by Special Counsel Robert Mueller, and said if asked he would provide Mueller with the nature of conversations shared with Trump.
"The President will continue to focus on his agenda that he was elected to pursue by the American people", the spokesperson said.More news: Arsene Wenger reveals Alexis Sanchez doubtful for Arsenal's game with Sunderland
- LeBron James Disappears as Celtics Win With 21-Point Comeback
- Arizona Diamondbacks 5, Chicago White Sox 4
- Palestinian 'Day of Rage' Protests Trump, Imprisonment and Imperial 'Peace' Calls
- Mueller cleared by US ethics experts to head Russia probe
- Manchester Bombing: Morrissey Slams Theresa May, Sadiq Khan And The Queen
- Sergio Aguero and Vincent Kompany will STAY at Manchester City
- Trump blames 'evil losers' for attack at Ariana Grande concert in UK
- Man detained outside Buckingham Palace in dramatic police swoop on the Mall
- Trump's Saudi Summit Was 'a Show Without Any Value' - Rouhani
- Philippines' Duterte leaves for 4-day visit to Russia