Nadler scheduled the hearing for Wednesday, Dec. 4, which will feature Constitutional law scholars.
The Democratic president of the House of Representatives, Nancy Pelosi, who will make the final decision, has not yet said whether the Republican president should be dismissed.
The Trump camp blasted out word of the ban in a statement from campaign manager Brad Parscale while the president was en route to Britain for a North Atlantic Treaty Organisation meeting.
Trump and Republicans continue to brand the accusations and process as a political "witch hunt".
Schiff has said "there's nothing for me to testify about", that he isn't a "fact" witness and that Republicans are only trying to "mollify the president, and that's not a good reason to try to call a member of Congress as a witness". He appeared on "Fox News Sunday".
The Judiciary Committee is expected to begin drafting articles of impeachment - which are the charges of wrongdoing against the president - in early December.
They have alleged that Trump tied a White House meeting and military aid for Ukraine to pressure the country's president, Volodymyr Zelensky, to probe former Vice President Joe Biden, one of the frontrunners for the Democratic presidential nomination, and his son, Hunter Biden.
That refusal has angered Democrats.
"It's straight forward to veil within the aid of a file, it's straight forward to veil within the aid of a gavel within the Intelligence Committee within the aid of-closed-door hearings". Collins reacts to a letter from Jerry Nadler asking whether or not Republicans want to subpoena witnesses to testify on behalf of the president.
According to testimony and a rough transcript of a July phone call by Trump to the Ukrainian president, Trump wanted Ukraine to announce investigations that would harm his political rival, Democrat Joe Biden, and bolster a debunked theory that Ukraine meddled in the 2016 USA presidential election.
Now that the president has declined to attend the hearing, it's unclear if the third phase will happen.
In his letter to Nadler, the White House counsel rejected the Democrats' argument that their impeachment inquiry is affording President Trump the same due process that President Clinton got during his impeachment proceedings.
"It is too late to cure the profound procedural deficiencies that have tainted this entire inquiry", he wrote.
"We can not justly expect us to participate in a hearing while the witnesses have not yet been appointed and although it is not clear whether the Judicial Committee will provide the President with a fair process through additional hearings", Cipollone wrote, according to a copy of the letter.
"'It's easy to hide behind a report, ' Collins said".
So far they have refused to testify, claiming "absolute immunity" as confidants of the president.
"It's easy to hide behind a report", said Rep. Doug Collins of Georgia, the top Republican on the judiciary committee.
"What I thought was really interesting is, in his letter, Adam Schiff does not mention any specific crime-no mention of bribery, no mention of extortion, no mention of quid pro quo", he said.
"Democrats are holding the most ridiculous political trial hearings in history".