Lugovoi, an ex-Kremlin bodyguard who London accuses of poisoning Alexander Litvinenko, a former FSB officer and Kremlin critic, with a fatal dose of radioactive polonium last November, took legal action over Kommersant's July article that he said portrayed him as a murderer.
On Wednesday, Kommersant representatives offered Lugovoi a clarification of the phrase that caused the court dispute, plus an interview in the newspaper.
"We will need about a month to study the draft agreement," lawyer Tatyana Stukalova, representing Lugovoi's interests, said.
The business paper wrote on July 9 that "after Britain's Crown Prosecution Service accused him of murdering... Litvinenko, Lugovoi was the first to speak about his victim's ties to British intelligence services."
Tatyana Stukalova said earlier: "My client believes by saying that 'Lugovoi was the first to speak about his victim's ties [with British intelligence services]' ... the paper imposed its viewpoint on its readers and portrayed Lugovoi as the culprit."
"We believe the article reports information that does not reflect the truth, and blemishes Lugovoi's dignity and business reputation," she said.
The chief of the Kommersant publishing house's legal service, Georgy Ivanov, said: "We will try to reach a compromise within a month's time... We will try to resolve issues, including financial ones, so that both sides are satisfied."
Lugovoi's lawyers, however, said Lugovoi called the draft agreement "senseless."
"At first sight, the proposals seem senseless, but I hope that by November 6, Kommersant representatives' reason and honesty will prevail," Lugovoi said, adding that he will insist on financial compensation whatever happens.
Russia's refusal to extradite Lugovoi to the U.K. has proved a major source of contention in relations between the countries, and in July sparked a tit-for-tat row involving expulsions of diplomats and visa restrictions.
Moscow has denied London's extradition requests, citing its Constitution, which bars the extradition of Russian nationals. Russian authorities said they could try Lugovoi at home if Scotland Yard investigators were to provide sufficient evidence.
In September, Lugovoi, a millionaire businessman who owns a private security company, confirmed that he would run for parliament as a candidate for the Liberal Democratic Party, led by outspoken pro-Kremlin ultranationalist Vladimir Zhirinovsky. Under Russian law, a seat in the State Duma would give Lugovoi immunity from prosecution.