"If we end up with a gridlock, I will say it if you can, Mitch, go nuclear," Trump said at the White House.
"That would be an absolute shame if a man of this quality was caught up in the web," Trump said of Gorsuch. "I would say it's up to Mitch, but I would say go for it."
The president also said he wants Gorsuch to be confirmed through an "elegant" and "dignified" process.
The nuclear option is a procedural move to overwrite a Senate rule with 51 votes, essentially eliminating any efforts of the minority party to filibuster. For now, Supreme Court nominees are still subject to the 60-vote threshold, but that could change if McConnell follows Trump's advice.
In 2013, when Congress was under Democratic control, the Senate voted to eliminate filibusters in the confirmation process for most executive and judicial nominees, lowering the vote threshold from 60 votes to 51.
McConnell, who was then the Senate minority leader, expressed frustration after the vote, calling it "a sad day in the history of the Senate."
"This was nothing more than a power grab in order to advance the Obama administration's regulatory agenda," McConnell said at a news conference on Capitol Hill on Nov. 21, 2013. "They just broke the Senate rules in order to exercise the power grab."
As Trump was speaking at the White House today, McConnell addressed his Democratic colleagues on the Senate floor, telling them to confirm Trump's Supreme Court pick with a clean majority vote.
"I would invite Democrats who spent many months insisting we need nine [justices] to join us in following through on that advice by giving the president's new nominee fair consideration and an up or down vote, just as we did for past presidents of both parties," McConnell argued.
After he spoke on the Senate floor, Senate Minority Leader Chuck Schumer argued that 60 votes is the "appropriate way" to go.
"Those who say that at the end of this process there are only two possible results — that the Senate will confirm this nominee or Republicans will use the nuclear option to change the rules of the Senate — are dead wrong," he said. "The answer will not be to change the rules of the Senate but to change the nominee to someone who can earn 60 votes."
He added, "On an subject as important as a Supreme Court nomination, bipartisan support is essential and should be a prerequisite. Sixty votes does that."
Schumer seemed to hint that the Democrats will not simply let Gorsuch sail through. Already some Democrats, such as Massachusetts' Elizabeth Warren and Ed Markey — have committed to opposing Gorsuch's confirmation.
"The Senate has a responsibility to weigh this nominee with the highest scrutiny, to have an exhaustive and robust and comprehensive debate on Judge Gorsuch's fitness to be a Supreme Court justice. We Democrats will ensure that it does," Schumer said.
Recently, when asked if he would consider getting rid of the filibuster should Democrats block Gorsuch's confirmation, McConnell said, "It's way too early for me to tell — or anybody else — what we might do."
"I think how this is handled depends on our Democratic friends," he said Sunday on ABC News' "This Week."
ABC News' Arlette Saenz and Ali Rogin contributed to this report.