"We have the votes," McConnell told reporters on Tuesday after a lunch meeting with colleagues in a show of Republican unity.
The impeachment trial is still in limbo as Republicans and Democrats remain locked in an impasse over its rules, reports Xinhua news agency.
Trump was impeached by the Democrat-led House of Representatives on December 18, 2019 for abuse of power and obstruction of Congress.
But the articles of impeachment haven't been delivered to the 100-member Senate, where Republicans have a narrow majority.
House Speaker Nancy Pelosi, who initiated an inquiry in September 2019 that led to Trump's impeachment, has tried to give the Democrats more leverage in negotiations with Republicans for setting the trial rules by holding up the articles of impeachment.
Senate Minority Leader Chuck Schumer has proposed calling on several witnesses during the Senate trial, while McConnell has so far rejected the demand, reiterating his stance on Tuesday.
"Fifty-one senators determine what we do and there will be, I'm sure, intense discussion, once we get past phase one, about the whole witness issue," McConnell said.
Schumer also said on Tuesday that Democrats would "force votes to put Republicans on the record".
"If Senate Republicans vote to prevent witnesses and documents, Americans will see it as a large and awful cover-up," the New York Democrat told reporters.
McConnell has said that the Senate should model Trump's impeachment trial after that of former President Bill Clinton, by dealing with potential witnesses once it begins.
In an anonymous complaint last year, a whistleblower raised concerns about the White House's interactions with Ukraine, resulting in the impeachment inquiry against Trump.
The President was alleged to have pressed his Ukrainian counterpart, Volodymyr Zelensky, into launching investigations that could politically benefit him. Furthermore, the White House has allegedly tried to cover it up.
Having repeatedly denied any wrongdoings, Trump slammed the Democrats for his impeachment at the White House on Tuesday.
"Whatever it is, it's a hoax. The impeachment is a big hoax," he told reporters. "It's become a laughing stock all over the world. There was nothing done wrong."
ccording to the nation's Constitution, the House has the sole power of impeachment, while the Senate can try all impeachments.
Conviction can only happen in the Senate and requires at least two-thirds of its members, or 67 Senators, to vote in favor after a trial.
Currently, the Senate has 53 Republicans, 45 Democrats and two Independents.
( With inputs from IANS )