The senators joined a growing, bipartisan group of lawmakers who have since publicly disputed Trump's accusation, which was made in a series of tweets more than two weeks ago.
The chair of the House Intelligence Committee, Republican Devin Nunes, has also said he has seen no evidence of wiretapping, but did not rule out the possibility of "incidental" surveillance, per CNN.
White House press secretary Sean Spicer on Tuesday said Trump is "extremely confident" that the Justice Department will produce evidence to back up his assertion.
In the latest twist it has been revealed that former national security adviser Michael Flynn, who was sacked last month by Mr Trump for lying about his connections to the Russian ambassador, was paid more than $33,750 (£27,300) by Russia's state-run broadcaster for giving a speech during the election campaign. Graham has previously said he would use subpoena power to get information from the Federal Bureau of Investigation about whether a warrant was issued allowing the Obama administration to tap Trump's phones during the campaign. "I don't think there was an actual tap of Trump Tower".
The New York Times article Trump references says the FBI has used intercepted communications in its investigation of several Trump associates and their ties to Russian Federation.
"The Department of Justice has complied with the request from leaders of the House and Senate Intelligence Committees and Judiciary Committees seeking information related to surveillance during the 2016 election", Justice Department spokeswoman Sarah Isgur Flores said Friday. That really covers, because wiretapping is pretty old fashioned stuff.
Britain's Daily Telegraph newspaper, citing unnamed intelligence sources, reported on its website that Spicer and Trump's national security adviser Lieutenant General Herbert McMaster had made formal apologies to Britain.
The accusations - flatly denied by Obama - were at first seen as frivolous, spur-of-the-moment comments after a politically bruising week, which Trump and his team could later retreat from without much damage.
They were among a list of names meant to speak at Monday's hearing but due to scheduling conflicts, that panel of witnesses is expected to appear March 28, Nunes said.
Trump said "the New York Times wrote about" Obama wiretapping him during the election.
Trump, in an interview Wednesday with Fox News, predicted there would be "some very interesting items coming to the forefront over the next two weeks".
I'd bet a good lawyer could make a great case out of the fact that President Obama was tapping my phones in October, just prior to Election! "This is Nixon/Watergate. Bad guy!", Trump tweeted.
Ryan told reporters he received the same intelligence briefing as Nunes and Schiff.