Comey wrote in private notes that Trump asked him to shut down the FBI's probe into former national security adviser Michael Flynn, and he also kept notes on a conversation in which he alleged Trump asked him for an affirmation of loyalty, people familiar with the documents have said.
Kellyanne Conway said the United States leader will make a decision on whether to invoke a doctrine called executive privilege.
A source told CNN on Wednesday Comey has spoken privately with special counsel Robert Mueller to work out the parameters for his testimony to ensure there are no legal entanglements as a result of his public account.
It is possible, the sources said, that a series of interactions, each of which the source said could have been considered a "ham-handed misstep", might be seen differently by the former FBI Director with the benefit of hindsight, not to mention his own firing.
Mr Comey was leading the FBI's probe into the allegations, and his firing sparked a political uproar.
On Wednesday, the House of Representatives Intelligence Committee approved subpoenas for Flynn and Trump's personal lawyer, Michael Cohen, in connection with its probe.
Democrats accused Trump of firing Comey to shut down the Russian Federation investigation, without acknowledging that they had also criticized his handling of Clinton's email scandal, with some even calling for his removal. Patrick J. Leahy, D-Vt., and Al Franken, D-Minn., released letters they had sent to Comey asking him to investigate whether then Attorney General-nominee Jeff Sessions broke the law in telling Congress, wrongly, that he had not had communications with Russians during the campaign.
On May 19, the Intelligence Committee announced that Comey has agreed to appear before the panel after Memorial Day.
However, a memo allegedly written by Mr Comey and reported in The New York Times suggested that the president asked him to end its investigation into Mr Flynn.
In addition to Russia's efforts to influence the presidential election, much of the questioning is likely to center around Comey's termination, which shocked senators in both parties. The White House has denied that a "conversation of that nature occurred".
Both the Senate and the House of Representatives also have committees conducting their own probes into possible ties between Russian Federation and the Trump campaign.