The project - already in the advanced planning stage - is aimed at silencing Russian politicians and ordinary people who often complain that the billionaire owner of the Premiership champions spends too much of his Russian-generated oil wealth in the UK.
It should also ensure that he stays on the right side of the Kremlin, from where Vladimir Putin, the President, has sanctioned uncomfortable investigations into the affairs of fellow oligarchs in recent years.
The prospect of a modern, state-of-the-art, national stadium should also help soothe Russian egos, which were badly bruised when the city failed to attract the 2012 Olympics.
The 55,000-seat venue will be built over three years. Mr Abramovich, 38, will put up the money for the multi-million pound project, but will expect to gradually recoup his investment from the stadium's ticket receipts.
Its primary role will be to host Russia's national team, whose mixed fortunes are followed closely by Mr Putin and are a perennial subject of joy and frustration for ordinary Russians, who are sceptical of oligarchs such as Mr Abramovich. The businessman's advisers say they hope that in time the stadium could host some of Europe's most prestigious tournaments such as the Champions' League.
Sources close to the football-loving tycoon say Mr Abramovich believes the stadium will go some way to improving his often controversial image in Russia, where many people resent his wealth, estimated at $14.7bn (£8.4bn). Many also question how anyone could have honestly built up such a vast fortune at a time when many people have seen their real incomes fall.
When a large chunk of that money was invested in a London football club in 2003, anger was compounded by frustration. Moscow's Mayor, Yuri Luzhkov, called the move a slap in the face for Russian football.
Sergei Stepashin, the head of Russia's Kremlin-controlled Audit Chamber, went further, criticising Mr Abramovich for lavishing too much money on English football at the expense of the Russian game. Subsequent press coverage of Mr Abramovich's high-rolling lifestyle and his fondness for super yachts and exclusive British properties have alienated ordinary people in Russia - a third of whom live below the poverty line.
Moscow's city fathers are expected to sign off on the stadium in the coming months. "We are waiting for an answer from the city government, everyone wants it," Artem Vagin, a spokesman for the Football Union of Russia, said yesterday. "Of course we're interested in this project. If someone offered to build a stadium for you, you'd take it."
A spokesman for Sibneft, the oil giant that is the source of much of Mr Abramovich's wealth, said that the stadium was just the latest in a long line of football-related projects funded by the oil tycoon.
"He has always been very supportive of Russian soccer," the spokesman told The Independent. "He funds Russia's football academy which has built pitches for youth teams around the country."
One of Chelsea's European rivals, Moscow's CSKA football team, also benefits from his patronage. Sibneft sponsors the club, which won the Uefa Cup in May, to the tune of some $18m a year.
The spokesman suggested the stadium project was further proof Mr Abramovich remains deeply committed to Russia and his native Moscow despite persistent rumours he is looking to sell his stake in Sibneft and relocate permanently to the UK. "He is a Russian government figure, a patriot and a regional governor. Talk of some kind of quick exit [from Russia] to England or of some kind of repatriation are exaggerated."
When asked whether the stadium project might help silence Mr Abramovich's domestic critics, he chuckled. "His critics have been pretty quiet since CSKA won the Uefa Cup. You would hope that this [the stadium project] would silence them."
That is open to question but what is not is that such grand gestures should ensure that Mr Abramovich avoids the fate of Mikhail Khodorkovsky, who used to be Russia's richest man but now spends his days in jail, contemplating a nine-year prison sentence for fraud and tax evasion.