Russian President Vladimir Putin could attempt to insert himself as an intermediary as tensions between the U.S. and Iran escalate, former U.S. Defense Secretary William Cohen told CNBC on Tuesday.

"I believe that President Putin is going to try and step in and be the peacemaker here," said Cohen, a Republican former senator from Maine who served as Pentagon chief under Democratic former President Bill Clinton.

"I think [Putin] is going to move in and say, 'Let me help solve this problem for you, Donald," Cohen added.

The U.S. military on Thursday night killed top Iranian commander Gen. Qasem Soleimani in a drone strike in Baghdad at President Donald Trump's direction. Iran vowed to retaliate.

Russia has recently warmed its relationship with Iran and gained a foothold in what the U.S. considers a rogue nation, Cohen said in a "Squawk Box" interview.

Putin already has plans to address the heightened hostilities between the U.S. and Iran. He is set to meet with German Chancellor Angela Merkel in Russia on Saturday, and spoke with French President Emmanuel Macron on Friday.

Germany and France are scrambling to keep talks with Iran over its 2015 international nuclear agreement alive despite Tehran having all but torn up the deal after the death of Soleimani.

Cohen, who founded the Cohen Group consultancy in 2001, said Russia could try to broker a deal over how Iran controls its nuclear facilities following Trump's 2018 decision to pull out from the Iran nuclear deal.

"I'm a bit more optimistic that the Russians will come in as a peacemaker," he said.

For Iran, Cohen said he sees Putin's potential intervention as an effort to get Americans to retreat from Iraq, a move that would help Russia strengthen its presence in the country, similar to what it did after U.S. troops pulled out of Syria.

Getting U.S troops out of Iraq would be "something that the Iranians want and something that the Russians would be happy with," Cohen said.

Russia is now a "major player in Syria and throughout the region," Cohen added. "They're going to come to the rescue at some point on Iran as well."