Senate Majority Leader Mitch McConnell (R-Ky.) on Tuesday shot down taking up legislation to block the Trump administration from unilaterally firing Robert Mueller, saying the special counsel isn't under threat.

"My understanding is there's no effort underway to undermine or to remove the special counsel. Therefore, I don't see the need to bring up legislation to protect someone who appears to need no protection," McConnell told reporters.

Asked what would happen if Trump tried to fire Mueller, McConnell said the question is a "hypothetical" and "as of right now I'm unaware of any effort, official effort, on the part of the White House to undermine the special counsel."

The New York Times reported late last week that Trump in June tried to fire Mueller - who is investigating the 2016 election and potential collusion between the Trump campaign and Moscow - but was stopped after White House counsel Don McGahn threatened to resign.

Democrats have latched onto the report, arguing it underscores the need for legislation protecting Mueller's job.

GOP Sen. Thom Tillis (N.C.) and Democratic Sen. Christopher Coons (Del.) introduced the Special Counsel Integrity Act last year, which would let Mueller or any special counsel challenge their firing in court.

A separate proposal from GOP Sen. Lindsey Graham (S.C.) and Democratic Sen. Cory Booker (N.J.) would require a judge to approve a Justice Department request to fire Mueller or any other special counsel.

But the bills face an uphill battle to getting 60 votes. Republicans are publicly supportive of Mueller but skeptical that the president would actually fire him.

Deputy Attorney General Rod Rosenstein named Mueller, a former FBI director, as special counsel for the Russia investigation after Trump fired then-FBI Director James Comey.