Sen. John McCain and a leading Democratic senator are calling on American and international soccer officials to reconsider the decision to hold the 2018 World Cup in Russia, casting it as a way to leverage power against Vladimir Putin in a way he's sure to understand.

McCain, a senior member of the Senate Foreign Relations Committee, told the ESPN/ABC podcast "Capital Games" that while the U.S. can play a leadership role in pressing for a new country to be chosen for hosting duties, there should be no boycott.

"It absolutely should be reconsidered, but I would hasten to add that a unilateral decision by the United States would not bode well," said McCain, R-Ariz. "I'd like to see the United States and others - say, the British perhaps and other countries - raise the issue in ordinary meetings, periodic meetings that they have. Say, 'We need to discuss this issue. Is it appropriate to have this venue in Russia at this particular time, and aren't there other countries that would be far less controversial?'"

Listen to the full episode of "Capital Games" HERE.

Sen. Chris Murphy, D-Conn., who has traveled to Ukraine with McCain and worked closely with him in support of the Ukrainian government, agreed that FIFA, the governing body of World Cup soccer, needs to press Putin by holding out the possibility that Russia would lose the 2018 World Cup.

"If in the face of a downed airliner, in the face of crippling sanctions from the European Union, Putin thumbs his nose at the international community and continues to send in arms and personnel into eastern Ukraine, then I'm not sure how you reward this guy and his government with a major, international competition," Murphy said.

"This guy is all about image and right now he's obsessed with this image as a crusading military aggressor - a tough guy. But he also wants the ability for people to come to Russia and to see what he has done and the country that he has built. I think that this could be a real blow to him," Murphy added. "It might in the end be even more consequential to him and his prestige than any individual sanction against his economy that the United States or Europe is contemplating."

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McCain said the value Putin sees in showcasing his country at worldwide sporting events was obvious at the Winter Olympics in Sochi earlier this year. It was also on display at the World Cup in Brazil earlier this month, where Putin was pictured receiving a ceremonial soccer ball from FIFA President Sepp Blatter to mark the fact that Russia has hosting duties next.

"Obviously, he is a man of mammoth ego. He is the closest thing to an all-out dictator that we have seen," McCain said of Putin. "His ego is mammoth, and any blows to his ego [are] strongly resented. But also, his behavior is basically - he has gotten away with, literally, with murder."

"Let us recognize and identify Vladimir Putin for what he is, and Russian behavior for what it is. And frankly that [losing the World Cup] will be the greatest blow to him, because he loves being on the world stage," McCain added.

The calls from McCain and Murphy echo those of top government officials in the U.K. and Germany, among other countries, who have called on soccer's international governing body to revoke the tournament from Russia in light of the nation's involvement in the crisis in Ukraine.

FIFA has dismissed such calls, arguing that keeping the tournament in Russia will foster international dialog that "can achieve positive change."

Sports Illustrated Senior Writer Grant Wahl said on the podcast that FIFA officials appear unlikely to bow to demands of political leaders, when the organization's sponsors hold the real sway. He said it was telling that FIFA proactively has said the World Cup will take place in Russia in 2018 and Qatar in 2022, despite recent controversy about those selections.

"I don't think anything that happens in the very near term is going to have an influence on FIFA deciding one way or the other," Wahl said. "FIFA's just a very insular organization and a lot of their top people don't to me seem all that troubled by the reputation that FIFA has. They simply look at the bottom line."

McCain noted that some countries, including the Netherlands, are hesitant to speak out against Putin more forcefully because they depend on Russia for energy resources. That puts more of an onus on the United States to use levers at its disposal, he said.

"There's no doubt that Vladimir Putin feels that he can literally get away with murder," McCain said. "He is responsible, in my view, for the shoot-down of that [Malaysian] airliner and the tragedy associated with it. So he's gotten away with murder. And look at it from his viewpoint, and all things considered, he's doing pretty well."

Preparing a location to host the World Cup can be a lengthy process, and both Murphy and Wahl agree it's time to prod Putin now, while there's still time to solicit proposals for alternative sites if he refuses to cooperate.

"You have to do it by the end of the year. … You can't take the chance that this guy is going to calm down and start behaving - because what if another Ukraine crisis erupts in the winter of 2017-2018?" said Murphy.

"If the World Cup was, say, a month from now, I don't think we would be sending teams to the World Cup and I don't think that Europe would either."

"Capital Games with Andy Katz and Rick Klein" is a part of the podcast series ESPN Perspectives, with original audio programming on issues across the sports world. The program explores the intersection of sports and politics, through interviews and analysis, and can be downloaded free via iTunes or on the ESPN website.

ESPN's Andy Katz and ABC News' Erin Dooley contributed to this report.