When President-elect Donald Trump takes the oath of office in about three weeks, he could set American foreign policy on a course that brings U.S.-Russian relations closer and leads to progress on the war against terrorism and the Syrian crisis. Foreign policy experts suggest that a "grand bargain" could be negotiated between Trump and Russian President Vladimir Putin, which could address the global terror war and resolution of the Syrian conflict. Yet any potential agreement comes amid high tensions between the two countries, as President Barack Obama announced retribution on Russia in response to alleged U.S. election tampering.

Putin has publicly dismissed U.S. intelligence claims of political hacking, which were widely seen as a way to undermine the U.S. government. But the Russian leader also commented on the need to improve relations between the two countries, agreeing with Trump that the situation "cannot get any worse" and that "together we will think about how to make things better." "When there's a change of leadership and other interests coincide, then things can actually improve pretty quickly," said Robert English, a specialist on Russia and director of the University of Southern California's School of International Relations.

Putin looked at his economy and said, 'You know what, I just cannot afford to continue to spend the kind of money that I am on the military and foreign adventures.' Edward Turzanski Foreign Policy Research Institute national security expert

There's been a pattern of Russian relations going sour in the past three U.S. presidential administrations, both Democratic and Republican. Some experts suggest Trump and Putin exchanging pleasantries is a positive step but may not be enough to fix the relationship that has suffered from long-standing differences over geopolitical issues.

Yet during Putin's Dec. 23 news conference, the Russian leader said he wanted a "business-like" relationship with the new administration. The Russians have "a real urgency to get back to normal economic relations and get these sanctions removed," said English, who worked in the Reagan administration as a Defense department policy analyst.

Russia's economy has been under stress due to low oil prices and Western economic sanctions stemming from Russian hostilities in eastern Ukraine and the 2014 annexation of Crimea. Russia's military campaign to prop up Syrian President Bashar al-Assad — which is at odds with U.S. interests — has also had an economic cost, as well as military casualties on the Russian side.

"Putin looked at his economy and said, 'You know what, I just cannot afford to continue to spend the kind of money that I am on the military and foreign adventures,'" said Edward Turzanski, an international policy and national security expert with the Foreign Policy Research Institute, a think tank in Philadelphia.

Syrian President Bashar al-Assad meets with Russian President Vladimir Putin at the Kremlin Palace in Moscow, October 21, 2015. Kremlin Press Office | Anadolu Agency | Getty Images

A moderate recovery in oil prices may help Russia in 2017, but foreign policy analysts suggest there are still reasons for Russians to improve ties — namely, the fight against global terrorism and the war against the Islamic State, commonly known as ISIS or ISIL. "Putin has a problem with Islamic extremists and so does the United States," said Turzanski, who worked in the U.S. intelligence community during the Reagan administration. The Russian envoy to Turkey, Andrey Karlov, was killed Dec. 19 in an attack in Ankara that Trump blamed on a "radical Islamic terrorist." The ambassador's assassin shouted, "Do not forget Aleppo," a reference to Syria's second-largest city, and the site of a bloody and lengthy campaign by the Syrian government and its Russian ally to oust rebels armed by powers including the U.S. and Gulf states.

"The battle for Aleppo is over," said USC's English. "We're not going to get what we wanted [in Syria], which was Bashar al-Assad removed. But there is a deal out there for a managed transition where we work with Russia instead of against Russia. And maybe then we can tackle some of the other problems."

A leaked Pentagon memo dated Dec. 1 from Trump's defense transition team was obtained by the publication Foreign Policy and revealed a top priority of the president-elect is to "develop a strategy to defeat/destroy ISIS."

Russia's Prime Minister Vladimir Putin speaks with then-ExxonMobil Chief Executive Officer Rex Tillerson on August 30, 2011. Alexey Druzhinin | AFP | Getty Images