Mr Litvinenko died in a London hospital in November last year
The Russian Prosecutor General's Office said the constitution did not allow for the extradition of its citizens.
However, it said it would consider the possibility that Mr Lugovoi could be put on trial in Russia.
UK-Russian relations have been strained since Mr Litvinenko died of exposure to the radioactive isotope polonium-210.
UK officials have said they expect full co-operation from the Russian authorities in bringing the perpetrators to justice in Britain.
It has taken Russia five weeks to give an official response, although Prosecutor General Yuri Chayka has repeatedly said that no Russian national would stand trial in Britain.
However, a statement from his office said Mr Lugovoi could be investigated "if the British side makes the corresponding inquiry and offers the necessary material for a criminal case".
Mr Lugovoi, himself a former Russian agent, denies the charges against him, and last month accused British secret services of being involved in the murder.
He says that either MI6, fugitive Kremlin opponent Boris Berezovsky or the Russian mafia were behind the killing.
The Russian Federal Security Service said last month that a criminal case had been opened based on remarks and information provided by Mr Lugovoi.