The Amateur Football League of Russia (AFL) has said it would support Abramovich in the April vote.
"He meets the criteria the best," the AFL said in a statement. "He knows the football world from inside and is an effective organiser and manager."
The position is available after the resignation of Vyacheslav Koloskov who was forced out after 25 years in the job by government officials unhappy with the way he was running the sport.
St Petersburg politician Vitaly Mutko, a close friend of Russian President Vladimir Putin, and former Soviet goalkeeper Anzor Kavazashvili, are the only people officially nominated to date, reports the BBC.
As well as owning Chelsea, Abramovich governs Chukotka, Russia's eastern-most province, and is also involved in running a charitable soccer fund in Russia.
The RFU general assembly is due to vote for the president on April 2.
