Donald Trump's victory in the U.S. presidential elections and the strengthening dollar has led to a rout in a number of emerging market currencies but the Russian economy is expected to benefit. "Russia should be a clear beneficiary, based on politicians' statements so far on both sides of the Atlantic, we believe stabilization is within reach," Deutsche Bank said in a research note.

"The U.S. president can remove sanctions by a National Security Waiver. We therefore see relative value trade opportunities in ruble, move to over-weight sovereign credit and selected corporates. In local bonds we favor Russia over South Africa and Turkey due to lower macro vulnerability, higher real rates and stronger disinflationary trend," the bank said in the note.

Russian President Vladimir Putin said over the weekend that U.S. President-elect Trump has confirmed to him that he was willing to mend ties, though he also said he would welcome President Barack Obama in Russia, according to Reuters.

Benefits for Russia?

"I think Trump's victory represents a life saver for Putin," Alastair Winter, chief economist at Daniel Stewart told CNBC via email. Trump offers Russia three benefits, he said, the most important is the lifting of sanctions which will feed through to a revival in economic growth. "We know the Italians are eager to lift sanctions, as are several German parties including the SPD. Of course, (Angela) Merkel and her CDU want to retain sanctions but would struggle to hold the line if the US lifts them and it could be a major election issue," Winter said. Secondly, the reduced influence on U.S. foreign policy of the neoconservatives who according to Winter remain as paranoid about Russia as ever. "This would in return reduce the likelihood of expensive Russian troublemaking in the Baltics, Western Ukraine, the Balkans and even in Western Europe. It may even help to share the cost of eliminating ISIS from Syria." The third and final benefit for Russia would be the international prestige that comes with being a superpower, Winter said, but the key question is when these benefits start to flow. "Prestige has already arrived in a pink bow. The Neocons will be difficult to displace even after Trump is in office and lifting the sanctions is far from certain. This explains why Russian assets rallied last week in the glow of the election result but have not since held on to all their gains."

What happens if sanctions are lifted?

However, analysts have warned that these assets remain poised for much larger gains if Trump does signal his intention to lift sanctions. While Trump's victory may have played a role in the rally in Russian assets, the ruble is enjoying support from higher oil prices ahead of an Organization of the Petroleum Exporting Countries (OPEC) meeting. The currency strengthened on the back of hopes that the OPEC countries will reach an agreement to cap or freeze oil output at a meeting scheduled for November 30. Russian President Vladimir Putin said over the weekend that Moscow was ready to freeze oil output at current levels.

"The ruble will tend to strengthen this week by corporate tax-related currency inflows and speculations about an OPEC production deal to be announced on 30 November. Nevertheless, the movements will be small, with USD/RUB staying in range 63.62–65.28," Per Hammarlund, Chief EM Strategist at SEB told CNBC via email. The ruble is currently trading at 64 against the dollar and is up by nearly 12 percent since the start of the year. However, the ruble is down more than 36 percent since the sanctions were imposed on Russia in late 2014. Meanwhile, analysts are waiting for more opportunities to arise in the coming months as relations between the U.S. and Russia start to stabilize. Deutsche Bank in its research note said that more opportunities can be seen in credit, foreign exchange and potentially rates.