Clinton, who flew here from Northern Ireland, also plans to advance negotiations for a new US-Russian nuclear arms reduction treaty as well as seek Russian help to promote Middle East peace and stabilise Afghanistan, aides said.
Her two-day visit to Moscow and the mainly Muslim city of Kazan is "part of ongoing efforts to rebuild an effective, constructive relationship with Russia," senior diplomat Philip Gordon told reporters on the plane to Moscow.
Making her first trip to Russia as chief US diplomat, Clinton is set to holds talks on Tuesday with her Russian counterpart Sergei Lavrov and President Dmitry Medvedev.
A US official said Clinton, who consulted British allies on Iran on Sunday, will ask the pair "what specific forms of pressure Russia would be prepared to join us and our other allies if Iran fails to live up to its obligations."
The senior State Department official, speaking to reporters on the condition of anonymity, confirmed that sanctions would be discussed as a form of pressure.
The United States, Russia, China, Britain, France — the five permanent members of the UN Security Council — plus Germany (the P5-plus-1) want Iran to halt its uranium enrichment programme, which the West fears masks a drive for a bomb.
Denying the charge, Tehran says the programme is for peaceful nuclear energy.
The United States, France and Britain in late September disclosed that Iran had hidden a second uranium enrichment plant near the holy city of Qom, raising further concerns about its intentions.
However, Iran has since struck a more cooperative tone by engaging the six powers in negotiations in Geneva earlier this month.
And Medvedev delighted the United States when he said sanctions are "sometimes inevitable" during a meeting in New York last month with President Barack Obama on the sidelines of the UN General Assembly.
The so-called P5-plus-1 has been instrumental in getting the UN Security Council to adopt three rounds of sanctions, although both Russia and China have until now resisted tougher sanctions.
"Certainly the cooperation from our Russian partners in the P5-plus-1 context is very encouraging," Clinton told reporters last week without elaborating. "We're going to get down to talking about what's the next step."
However, Clinton has stopped short of saying whether she believed Russia has had a change in heart toward sanctions.
The official also said Clinton wants to discuss a proposal in which Iran could ship uranium to Russia for enrichment there, which would ease concerns about what it would be used for.
A source familiar with the US-Russian talks on Iran told the Kommersant daily on Monday "we are ready for sanctions only in the event that there are no significant changes for the better in the foreseeable future."
Clinton and Lavrov are also expected to discuss missile defence and negotiations to replace the 1991 Strategic Arms Reduction Treaty (START).
Lavrov has called for "full clarification" about the new sea-based missile defence system.
The Obama administration unveiled the plan last month to replace an earlier version, backed by George W. Bush, to deploy missile defence facilities in Poland and the Czech Republic. Russia fiercely opposed Bush's plan.
START, which places strict limits on the US and Russian arsenals and is seen as a cornerstone of Cold War-era strategic arms control, expires on December 5 and negotiators have been seeking to thrash out a successor agreement.
Also on the broad agenda of what analysts describe as sometimes tense but improving ties are talks on Russia's alleged human rights abuses as well as multilateral efforts to promote Arab-Israeli peace and combat climate change.
Russia is the last stop on a five-day tour that has taken her to Zurich, London, Dublin and Belfast.
