The House Judiciary Committee is scheduled to hold another hearing on Monday. But a senior administration official said after the two-paragraph letter was released that that was the point it was meant to communicate.
Nadler has rejected those requests, saying all three people are "irrelevant" at this point.
Nadler mentioned on CNN that his committee hasn't determined what to incorporate within the articles of impeachment however will "take a lot of considerations into account".
Democrats are working through the weekend as articles are being drafted and committee members are preparing for a hearing Monday.
White House counsel Pat Cipollone informed the Judiciary Committee late Friday that the administration would not be participating in upcoming House hearings.
"A president who perverts his role as chief diplomat to serve private rather than public ends has unquestionably engaged in "high crimes and misdemeanors" - especially if he invited, rather than opposed, foreign interference in our politics", the Judiciary Committee Democrats said in their report on Saturday.
"They have had adequate time (to call witnesses)", Nadler told Bash, referring to House rules that require him to give Republicans a day to call their own witnesses.
The senior Republican on the Judiciary Committee, Doug Collins, announced a list of witnesses his camp wishes to subpoena, including Joe Biden's son, Hunter Biden, and his business partner Devon Archer.
The committee could draft and recommend the articles by next Thursday and the House could vote on them by Christmas. That's what we have now, an impeachment that will move forward based on what they believe to be the President's "real reasons" for holding back aid from Ukraine for a period of review.
The report covers the "constitutional grounds for presidential impeachment", including bribery, abuse of power, betrayal of America's national interest and corruption.
Nadler would not speculate on what might be included in the articles of impeachment.
"So you are willing to impeach the President with no Republican votes, correct?"
Judiciary Committee Democrats have said they could instead use Mueller's findings to demonstrate a repeated pattern of misconduct by Trump to support formal charges of abuse of power and obstruction of Congress.
Hunter Biden joined the board of Ukrainian energy company Burisma while his father was vice-president. Trump denies any wrongdoing but has refused to cooperate with the inquiry, citing his privilege as president to prevent top aides from testifying.
Cipollone issued the letter minutes before a deadline to declare whether the White House would deploy representatives to defend Trump against accusations he abused his office by pressuring Ukraine to find dirt on former vice president Biden, his potential challenger in the 2020 election.
She asserted that it seems that not a single Republican will vote in favor of the Articles of Impeachment being drafted by the House Judiciary Committee, although former GOP Representative Justin Amash of MI, who now identifies as an independent, has voiced his support.
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