Democrats must approve any requests made by Republicans and are required to reject Hunter Biden's and informants' summons requests.
CNN contacted lawyers for the informant and Hunter Biden for comment.
In the letter, the representative of California, Devin Nunes, the top Republican of the House intelligence committee, criticized what he called a "fictitious impeachment process". Nunes wrote that Republicans were calling witnesses to testify in an open environment to "provide transparency to your otherwise opaque and unjust trial".
The House Democrats are advancing with their investigation into the allegations that Trump pushed the Ukraine to investigate Joe Biden, son of the former vice president and the 2016 elections in order to politically help the President and that the White House has taken steps to cover it. Trump has denied doing anything improper.
Trump put forward an unproven allegation that he was then vice president Biden improperly tried to help his son by putting pressure on the Ukrainian government to dismiss the country's attorney general. At the time, Hunter Biden was on the board of the Ukrainian natural gas company.
There is no evidence of wrongdoing by Joe or Hunter Biden in Ukraine.
Biden's presidential campaign declined to comment on CNN's Saturday testimony request from the son of the former vice president. Joe Biden was asked on Friday in New Hampshire if he himself would testify in a Senate impeachment trial if asked – although the Republicans have not yet made such a request.
"Let's focus on the problem here," Biden said. "The question is: did the President of the United States violate the Constitution … And did he profit from his office?" He again invited Trump to release his tax returns.
They intensified efforts to strengthen a key strategic alliance after Trump enlisted his own personal lawyer, Rudy Giuliani, to work outside the normal diplomatic channels in an obvious attempt to strengthen his chances for re-election.
Jeremy Herb, Manu Raju and Marshall Cohen of CNN contributed to this report.