Former US Defense Sec: Republicans want to ‘follow the money' on Russian relations

President Donald Trump will not be able to improve relations with Vladimir Putin until the Republicans "follow the money" to better understand Washington's ties with Moscow, according to a former U.S. Defense Secretary.

Relations between the U.S. and Russia have been strained by claims that people connected to the Trump administration have had inappropriate relations with Russian counterparts and that Moscow may have helped Donald Trump win the U.S. general election.

Prior to that, relations had already faltered after Russia annexed Crimea in 2014.

Former U.S. Defense Secretary William Cohen told CNBC Monday that any ties between the two countries will continue to be strained by uncertainty.

"President Trump will find it hard to move ahead with Republicans in the Senate saying 'Wait a minute, we want to investigate, we want to follow the money, and we want to look at Mr. Manafort and others.'"

U.S. lobbyist and consultant Paul Manafort is currently under investigation by the FBI, CIA and National Security Agency. As well as working on several U.S. Republican campaigns, Manafort has worked as an adviser on the Ukrainian presidential campaign of Viktor Yanukovych, whose direct ties to Russian president Vladimir Putin was one of the reasons for his ouster in 2014.

"There's something here that doesn't quite measure up," said Cohen who added that clearing up and explaining any exchange of cash would be key to ending the U.S./Russian saga.

"I don't think President Trump will be able to have a reset with President Putin until the issue of money, and the trail of money is resolved."

Cohen added there was now a "cloud hanging over the Trump administration" as people questioned how the U.S. could move forward with Moscow.

"Namely that you could embrace Putin given what he's done in Crimea, given the fact he's tried to destabilize Ukraine, given the fact he's tried to cause some anxiety in the Baltic etc., and it's inexplicable at this point, so I think he's [Trump] going to have to be more forthcoming."

Cohen told CNBC that Trump's temperament as a president was not one he had ever witnessed before but there were signs that he is beginning to understand his role as president.

"I think he's also learning you can't be a CEO of the US and conduct it as if it were the Trump business empire," he said.

"It's a learning process which I think he's unfamiliar with and has not had to deal with in the past, and is something he's softening his rhetoric to some degree, and changing his positions based on the advice that he's getting from very, very good choices you have in the National Security Field," he said.

In a Gallup poll released Sunday, Trump's approval rating had sunk to 37 percent.