As reported by Censor.NET citing Reuters, he said in an interview with The Times of London.
Trump has slammed Russia's campaign in Syria, claiming it has led to "terrible humanitarian situation."
"They have sanctions on Russia - let's see if we can make some good deals with Russia," the Republican president-elect was quoted as saying by The Times. "For one thing, I think nuclear weapons should be way down and reduced very substantially, that's part of it. But Russia's hurting very badly right now because of sanctions, but I think something can happen that a lot of people are gonna benefit."
Trump said he would start his work as U.S. president having confidence in Putin and German Chancellor Angela Merkel, though the attitude may change quickly.
He offered criticism against Merkel for what he said was a disastrous mistake to allow millions of migrant workers to arrive in Germany.
On Britain's vote to leave the European Union, Trump said: "Brexit is going to end up being a great thing" and said he was eager to get a trade deal done with the United Kingdom.
He also invited Prime Minister Theresa May to visit the White House immediately after taking office.
Trump believes other EU countries will follow Britain's example as the migrant crisis has affected the block a great deal.
He also promised to strengthen the U.S. border, including through restrictions on entry for Europeans as well as a tough control of all immigrants entering the United States from countries stricken with Islamic terrorism.
Trump also blasted the U.S. foreign policy, saying the decision to invade Iraq was probably the worst decision in the history of the country.