Lebedev has held talks with DMGT for more than a year and is believed to be seeking 75% of the Standard, plus one share.
An announcement on the deal is expected within the coming days.
Lebedev told Bloomberg News: "This is not my way to make money, but I'd like to explain to the public that newspapers are something they should love and cherish.
"I have an interest in serving the case of defending the freedom and independence of print media."
He said he would not take an active part in the news content of the Standard, but would be in charge of the financial side.
The Russian billionaire was a former lieutenant-colonel in the KGB but left the service to become a banker and now heads the National Reserve Bank in Russia.
He founded Moscow news magazine Korrespondent and a part-owner of the Novaya Gazeta paper, which is one of the latest sources of media opposition to the corruption in Russia.
The Standard is the only paid-for evening paper in London but is believed to lose between £10m and £20m a year. The paid-for circulation of the title has dropped markedly since the arrival of the London freesheets -- the London Lite and thelondonpaper -- in September 2006.
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