If Mr Lugovoi wins he would be mayor right up to the 2014 Winter Olympics
Andrei Lugovoi, the prime suspect in the murder of Kremlin critic Alexander Litvinenko, is set to run for mayor of the southern Russian city of Sochi.
The Liberal Democratic Party of Russia is backing Mr Lugovoi as its candidate, although it has not yet registered him.
British police want to question Mr Lugovoi, who is already an MP, about Mr Litvinenko's death by radioactive poisoning in London in November 2006.
Moscow has said Russia's constitution bars any extradition.
It has asserted that Mr Lugovoi was framed by the British Secret Intelligence Service (SIS), also known as MI6.
But senior British officials told the BBC in July that they believed the murder was carried out with the backing of the Russian state.
Mr Litvinenko, a former KGB officer, fell ill shortly after a meeting at a central London hotel with Mr Lugovoi. He was later found to have been poisoned with the radioactive substance, polonium-210.
Alexander Litvinenko died in London in 2006 shortly after being poisoned
In May 2007, the UK's Crown Prosecution Service formally submitted an extradition request to Moscow for Mr Lugovoi to stand trial in the UK. This remains current, but Russia has so far refused to co-operate.
Mr Lugovoi, a former KGB bodyguard, has denied any involvement in the killing.
In the meantime, he has become a national politician after being elected to the Duma as a deputy for the Liberal Democratic Party.
On Friday, the nationalist party said it was now considering whether to put him forward as their candidate for mayor of Sochi on Russia's Black Sea coast.
The leader of the party's parliamentary faction told the BBC that Mr Lugovoi was its most likely candidate.
The election will be held next month and if Mr Lugovoi wins he would be mayor right up to the opening of the Winter Olympics in 2014.
Mr Lugovoi said he viewed the initiative with curiosity and interest. When asked if he would visit London if he became mayor of Sochi to learn about preparing for the Olympics, he said if necessary he would.
Mr Litvinenko's widow, Marina, said the election of Mr Lugovoi would be "an affront to all people of good will".
"In that case I would call for a boycott of the games. I would personally go from country to country urging people not to go to an event hosted by a murderer," she said in a statement.