US Speaker of the House Nancy Pelosi holds a press conference after the House passed Resolution 755, Articles of Impeachment Against President Donald J. Trump, at the US Capitol in Washington, DC, on December 18, 2019. -

"We can't name managers until we see what the process is on the Senate side and I would hope that would be soon. So far, we haven't seen anything that looks fair to us," Pelosi said.

In a press conference following the historic vote Wednesday night , Pelosi told reporters on Capitol Hill she wanted to see how McConnell, R-Ky., would lay out the trial's rules before she sent over the articles to the Senate.

After the House voted to impeach President Donald Trump, Speaker Nancy Pelosi began a game of chicken with Senate Majority Leader Mitch McConnell.

Pelosi's stance was an apparent attempt to pressure McConnell, who will hold significant power once the impeachment proceedings are passed from the Democrat-led House to the GOP-controlled Senate.

McConnell did not respond to CNBC's request for comment.

The House voted to impeach Trump nearly along party lines on articles of abuse of power and obstruction of Congress. The Constitution mandates that the Senate will conduct a trial to decide whether to convict Trump and remove him from office.

As part of the Senate trial, House Democrats will select so-called impeachment managers to appear before the Senate and share findings from their three-month inquiry into Trump's Ukraine dealings. House managers have historically been members of Congress, who assume the role of prosecutors in the Senate trial.

There is no set time frame for Pelosi to follow to carry out this step. But she suggested Wednesday night that she will hold off until she receives assurances about the Senate trial proceedings.

"This is what I don't consider a fair trial," she said when pressed by reporters. "That leader McConnell has stated that he's not an impartial juror, that he's going to take his cues, in quotes, from the White House, and he's working in total coordination with the White House counsel's office."