The move coincides with an urgent visit to Washington by NATO Secretary General Mark Rutte, who will meet President Donald Trump and key lawmakers the same day.
If passed, the bills would empower bipartisan senators to act more forcefully against Moscow and signal Congress's readiness for decisive steps, the report said.
Committee Chairman Sen. Jim Risch (R-Idaho) told Axios: "The more we can do here to counter Russia, the more we seek to do it."
Sen. Jeanne Shaheen (D-N.H.), a committee member, added: "Since the White House seems unwilling to act, I think it's important for Congress to take certain steps, and I'm very glad that for the first time this year we have bills that will make it harder for Russia to wage this war."
The committee is expected to consider three bills: one designating Russia a state sponsor of terrorism for abducting Ukrainian children; a second imposing economic sanctions on China for supporting Russia's war in Ukraine; and a third allowing the use of frozen Russian assets in the United States, with transfers to Ukraine every 90 days, Axios reported.
On Oct. 20, Senate Republican Leader John Thune said the chamber would delay consideration of a Russia sanctions bill until after Trump's summit with Russian President Vladimir Putin.
Trump described a "productive" Oct. 16 call with Putin and announced an in-person meeting in Budapest within two weeks.
The president also said he agreed with Putin on a high-level meeting between U.S. and Russian advisers next week.
CNN, citing a White House representative on Oct. 21, reported that a Rubio-Lavrov meeting scheduled for this week has been postponed "for some time."
Later that day, an NBC News journalist said planning for the Trump-Putin meeting is on hold. Unnamed diplomats told Reuters that Russia's refusal of an immediate ceasefire in Ukraine appears to threaten the Trump-Putin summit.
The Financial Times, citing sources on Oct. 21, reported that Rubio and Lavrov will arrive in Budapest on Oct. 30.
Trump told White House reporters after his Oct. 16 call with Putin that now is not the "perfect timing" to strengthen U.S. sanctions against Russia.
On Sept. 14, Trump said European Union sanctions against Russia "aren't tough enough." He emphasized he is ready to impose sanctions but expects Europe to match the level.
In a joint interview with Reuters and Bloomberg, U.S. Treasury Secretary Scott Bessent said the war in Ukraine could end in 60-90 days if European countries imposed major sanctions on buyers of Russian oil.
Politico reported that Trump could halt Russian oil imports to the EU "with one phone call" to his allies — Slovak Prime Minister Robert Fico and Hungarian Prime Minister Viktor Orban.
On Oct. 11, Trump said the United States is imposing 100% tariffs on all goods from China and export controls on critical software.