"That's an appropriate subject for the Senate Intelligence Committee to take a look at," he said during a Playbook Live interview on Thursday.
The Senate Intelligence Committee is already probing Russia's meddling in the presidential race, and the White House has floated the idea that the president's claim be folded into the larger investigation.
Trump appeared to catch lawmakers off guard over the weekend when he tweeted, without evidence, that his predecessor "had my 'wires tapped.'"
Terrible! Just found out that Obama had my "wires tapped" in Trump Tower just before the victory. Nothing found. This is McCarthyism!— Donald J. Trump (@realDonaldTrump) March 4, 2017
McConnell said Thursday he has seen "no evidence" to support Trump's claim.
A Senate Judiciary subcommittee overseen by Sens. Lindsey GrahamLindsey Olin GrahamA pandemic of hyper-hypocrisy is infecting American politics Republicans' mantra should have been 'Stop the Spread' Senators preview bill to stop tech giants from prioritizing their own products MORE (R-S.C.) and Sheldon WhitehouseSheldon WhitehouseSenate GOP signals they'll help bail out Biden's Fed chair The Hill's Morning Report - Presented by Altria - Jan. 6 panel flexes its muscle Sen. Whitehouse blasts Alito speech: 'You have fouled your nest, not us' MORE (D-R.I.) is already probing Trump's allegation.
The two sent a letter to top Justice Department and FBI officials on Wednesday requesting any warrant application or court documents that would show that Obama ordered surveillance on the Trump campaign.
Democrats are pushing for a special prosecutor to handle the probe into any ties between Moscow and the Trump campaign.
Republican senators, however, have dismissed that effort. Senate Judiciary Committee Chairman Chuck GrassleyChuck GrassleyLawmakers pay tribute to Colin Powell Senate GOP signals they'll help bail out Biden's Fed chair Fill the Eastern District of Virginia MORE (R-Iowa) during a hearing this week argued it was too soon to know if a special prosecutor is necessary.
McConnell echoed that on Thursday, calling the Democrats' demand "way, way premature."
"I think Senator Warner and Senator Burr can handle this," he said of the intelligence panel leaders.