The law would be based on an existing scheme in the Russian region of Belgorod where police hand out on-the-spot fines for anyone overheard using foul language in public.
The fines range from 10 pounds to 30 pounds. People heard cursing in front of children are fined the most.
Mikhail Nikolayev, deputy chairman of Russia's upper house of parliament, or Federation Council, is pushing the improbable initiative.
"Swearing should cease to be part of our everyday life," the Telegraph quoted him as saying.
The scheme in Belgorod, started in 2005, has produced encouraging results.
Kremlin government has stepped up efforts to tackle rampant alcoholism, a culture of heavy smoking, and a steady stream of hardcore violence and erotica on TV and in adverts.
A clutch of fellow senators is supporting Nikolayev's plan.