"The Russians had said that, right after the election, that they had been meeting regularly with people from the campaign," Franken told ABC News' Jon Karl and Rick Klein on the "Powerhouse Politics" podcast. "Now, you can't trust anything the Russians say. But on the other hand, it's really hard to trust anything that Donald Trump says ... you can't rely on anything he says."
The comments come amid unsubstantiated allegations from a dossier given to the FBI that suggested Trump could have been compromised by Russian agents and could have communicated with Russian hackers during the 2016 campaign. The dossier provides no evidence.
"Trump was so positive toward Putin and toward Russia and has been that, you know, you kind of have to wonder why," Franken continued, speculating that it's possible Trump's relationship with Russia is "worse" than that outlined in the unsubstantiated dossier.
The document was reportedly included in classified intelligence briefings to President Barack Obama and President-elect Trump last week.
Independent Sen. Angus King of Maine told Karl and Klein that the investigation into Russia's role in the 2016 election must continue despite the beginning of Trump's tenure in the Oval Office.
"I think it's in [Trump's] interest, as well as the country's, to get to the bottom of this as soon as possible," King said on the podcast. "I do think allegations, particularly of contact between the Trump campaign and the Russians, is potentially grave and serious and has to be run down. Now, once we get to the bottom of what happens, then, nobody knows. Nothing like this has ever happened before."
"I think it would be very difficult, if not impossible, for a presidential administration to shut down an investigation of this nature," King continued. "I mean, ask Richard Nixon if you could shut it down. I just don't think it's possible."
On Republicans' plans to repeal and replace the Affordable Care Act, Franken blasted GOP leaders over the lack of a clear path forward. "I heard [Speaker Paul] Ryan saying we had a lot of plans," he started. "A lot of plans -- it's like a quarterback going back into the huddle and saying, OK guys, we're going to run four plays on this down ... it's just chaos."
Franken also hit Trump over his recent press conference. "I'm afraid it may be the new normal," he said. "To me, that press conference was disturbing."
On Thursday's news that the Justice Department's independent watchdog plans to probe, among other things, FBI Director James Comey's public comments on the Hillary Clinton email investigation, King said it was an "important question" but at this point it's only an "interesting exercise for historians."
"I have to be honest: There's so much else going on it seems like history at this point," King said. "I think, in retrospect, it was a poor decision because he was talking about an ongoing investigation."
Both Franken and King also expressed concerns over some of Trump's nominees. "I personally am very very unhappy on a number of things," Franken said about Sen. Jeff Sessions, R-Alabama, Trump's pick for attorney general. "On certain areas, he needs to be independent of the president," he continued, saying that Sessions needs to be the "lawyer for everybody."
King said he was "inclined to" back Republican Rep. Mike Pompeo's nomination for CIA director, but had concerns about Sessions and Rex Tillerson, Trump's pick for secretary of state. "I have to admit that there were some things he said that really sort of bothered me," King said on Tillerson. "I went into the hearing ready to be supportive, but I came out still in doubt."