Russia's attempt to influence elections is nothing new, former CIA Director James Woolsey told CNBC on Thursday. But the United States should take a novel approach in how it retaliates, he said.

"The Russians have been doing this for decades in one way or another," Woolsey, who is now a partner at Lux Capital Management, said in an interview with "Power Lunch" from the sidelines of the YPO Edge summit in Vancouver, British Columbia.

Woolsey, who served as director of the CIA under President Bill Clinton, said Russian intelligence normally goes after different religious groups, as well as elections around the globe.

"What's new is to use cyber in … trying to influence their neighbors' elections, including us. And that's something we shouldn't put up with," he said.

Woolsey thinks that instead of just investigating the role of Russian intelligence, the U.S. should go after Russia where it hurts — its economy. He suggests automobiles in the U.S. have the ability to use more than one fuel, such as methanol or wood alcohol, so that when drivers fill up, they have a choice.

"That would make the Russians very unhappy and I think probably a lot more willing to be decent."

U.S. intelligence agencies have concluded that Russia used hackers to try to meddle in the 2016 U.S. election. There have also been questions about contacts between those in President Donald Trump's camp and Russian officials.

On Wednesday night, it surfaced that Attorney General Jeff Sessions had conversations with the Russian ambassador to the United States during the presidential campaign.

On Thursday, Sessions told NBC News that he did not meet with "any Russians at any time to discuss any political campaign." His spokeswoman said the discussions came in his capacity as a senator on the Armed Services Committee.